29 results on '"Abbagari, Souleymanou"'
Search Results
2. Peculiar optical solitons and modulated waves patterns in anti-cubic nonlinear media with cubic–quintic nonlinearity.
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Houwe, Alphonse, Abbagari, Souleymanou, Akinyemi, Lanre, Rezazadeh, Hadi, and Doka, Serge Y.
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OPTICAL solitons , *SOLITONS , *QUINTIC equations , *NONLINEAR Schrodinger equation , *ROGUE waves , *WAVENUMBER , *NONLINEAR waves , *TRIGONOMETRIC functions - Abstract
In this work, we investigate diverse analytical solutions and modulation instability of the nonlinear Schrödinger equation with an anti-cubic nonlinear term. We use the traveling wave transformation and the New Generalized Extended Direct Algebraic Method to perform a variety of exact traveling wave soliton-like solutions. The obtained solutions are among other trigonometric function solutions, complex soliton solutions, and rational solutions. A particular behavior has been depicted in self-focusing and defocusing nonlinearity where dark soliton changes to super rogue waves and breather soliton is obtained. We then use the linearizing scheme to get the growth rate of modulation instability. For a specific value of the excitation wave number and a specific time of simulation, diverse waveforms of the modulated waves are obtained. We have demonstrated that the combined dispersion and nonlinear terms, as well as the anti-cubic nonlinear term, can develop modulation instability. To confirm the predictions based on the analytical results, we use the direct numerical simulation, from which we have displayed a modulation wave of the growth rate modulation instability. It results equally that the anti-cubic nonlinearity is an important object to control the propagation of the solitonic waves in the nonlinear systems. [ABSTRACT FROM AUTHOR]
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- 2023
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3. Synchronized wave and modulation instability gain induce by the effects of higher-order dispersions in nonlinear optical fibers.
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Abbagari, Souleymanou, Houwe, Alphonse, Akinyemi, Lanre, Inc, Mustafa, Doka, Serge Y., and Crépin, Kofané Timoléon
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OPTICAL solitons , *OPTICAL fibers , *OPTICAL dispersion , *NONLINEAR Schrodinger equation , *YIELD strength (Engineering) , *TELECOMMUNICATION systems - Abstract
This work examines the effects of the higher-order dispersion (HOD) on modulated waves and modulation instability (MI) gain by using the perturbed nonlinear Schrödinger equation having the cubic quintic septic nonlinearity. We use the new generalized auxiliary equation method to underline the behavior of bright, dark soliton as well as the combined optical soliton solutions. Considering the constraint relation on the combined optical soliton solutions, we carry out the W-shaped profile. We observe that the obtained optical soliton solutions can spread without alteration and can preserve their shapes. Moreover, we enhance the obtained analytical results by using the Split-Step Fourier technic which yields points out stable optical solitons. We have obviously highlighted the effects of the HOD by means of the numerical simulation. Owing to the fact that the model has nonlinear and dispersions terms, we have shown how the MI growth rate and the modulation bands can expand under the influence of the HOD terms in normal and anomalous dispersion regimes. It is worth mentioning the appearance of the unstable zones when the value of the higher-order dispersion term increases and additional bands also emerges. Compared these results with some previous works (Kohl in Optik 203:163451, 2020; Yao in Res Phys 30:104825, 2021; Wang in Phys Lett A 372:417–423, 2008; Ismail in Appl Math Comput 209:425–429, 2009; Nestor in Eur Phys J Plus 135:380, 2020), additional bands of the MI have been pointed out while the MI gain spectra have shown new sides lobes. We expect that these relevant and concise results could probably help to improve the communication system through optic fibers. [ABSTRACT FROM AUTHOR]
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- 2022
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4. W-shaped profile and breather-like soliton of the fractional nonlinear Schrödinger equation describing the polarization mode in optical fibers.
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Houwe, Alphonse, Abbagari, Souleymanou, Djorwe, Philippe, Saliou, Youssoufa, Doka, Serge Y., and Inc, Mustafa
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We use the fractional nonlinear Schrödinger equation (FNLSE) to describe the polarization mode in optical fiber with Self-Steepening, Self-Frequency Shift, and Cubic-quintic terms to analyze the effects of the fractional time parameter (FTP) on bright and dark solitons as well as breather-like solitons. We use the transformation hypothesis and auxiliary equations method to obtain three families of solutions such as combined bright soliton, dark solitons, and rational solitons. We have shown the effects of the fractional parameter (FP) on the W-shaped profile, bright and dark optical soliton solutions as well as the corresponding chirp component. It is observed that for small values of the FP, optical soliton shape is affected and the soliton is unstable. Moreover, one observes the effects of fraction time on Modulation Instability (MI) gain spectra and MI bands. For certain values of the FP, it is formed sides lobes and for specific small values of the FP, both stability zone increases and amplitude of the MI gain increase while the stability zones increase. To confirm the robustness of the analytical results, we have used a numerical investigation. One exhibits the formation of breathers-like soliton with stable amplitude for small values of the FTP. It results from this study that the FP is efficient and can be used as an energy source where soliton or breathers-like soliton are involved for communication in optical fibers. [ABSTRACT FROM AUTHOR]
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- 2022
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5. Solitonic rogue and modulated wave patterns in the monoatomic chain with anharmonic potential.
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Houwe, Alphonse, Abbagari, Souleymanou, Akinyemi, Lanre, and Crépin, Kofané Timoléon
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ROGUE waves , *NONLINEAR Schrodinger equation , *WAVENUMBER , *PLANE wavefronts - Abstract
Modulation instability and rogue wave structures have been investigated in this work. This study is an extension of the work in Abbagari (2023), where a nonlinear Schrödinger equation with higher-order dispersion is derived to show only the development of the modulated waves bounded to bright soliton as a nonlinear exhibition of modulation instability. Here, the coupled nonlinear Schrödinger equation is derived by using the multi-scale scheme. An overview of the analytical calculations of the perturbed plane wave is carried out to show the effects of the nonlinear chain parameters on the modulation instability growth rate and bandwidths. The interest of this study lies equally in the nonlinear modes of excitation, where solitonic waves are generated under certain conditions in lower and upper frequency bands. On the other hand, relevant results have been developed to show the features of the type I and type II rogue waves of the Manakov system. Such investigations are obtained under the variation of the interaction potential parameters and the free parameter of the similarity method. Via a numerical simulation, rogue wave structures have been generated as a consequence of the long-time evolution of the perturbed plane wave. At a specific time of propagation, another localized object has been obtained to show the Akhmediev breathers and Kuznetsov-Ma solitons clusters under a strong perturbed wave number. These results have opened up new features, and many applications could follow in the future. • Modulation instability (MI) and rogue wave (RW) have been investigated in this work. • The CNLSE is derived by using the multi-scale scheme. • The effects of chain parameters on the MI growth rate and bandwidths have been shown. • The features of the type I and type II RWs of the Manakov system have been show. • Via a numerical simulation, RWs structures have been generated. [ABSTRACT FROM AUTHOR]
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- 2024
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6. Brownian motion effects on W-shaped soliton and modulation instability gain of the (2+1)-dimensional nonlinear schrödinger equation.
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Abbagari, Souleymanou, Nyawo, Pélérine Tsogni, Houwe, Alphonse, and Inc, Mustafa
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NONLINEAR Schrodinger equation , *WIENER processes , *MODULATIONAL instability , *BROWNIAN motion , *IMPACT strength - Abstract
Investigation of soliton solutions and Modulation Instability (MI) analysis to the (2+1)-Stochastic Chiral Nonlinear Schrödinger Equation (SCNLSE) having noise force and Brownian movement (BM) have been done in this work. We first use the transformation technic and auxiliary equation method (AEM) to establish three types of soliton solutions. Depending on the constraint relation set on the auxiliary equation parameters, it is obtained bright and dark soliton solutions. Thereafter, taking the same different parameters it is gained the combined bright-dark soliton, bright-bright soliton solutions. By employing suitable values of the used parameters together with the model parameters it is show out W-shaped soliton solutions. Throughout the paper it is clearly established the impact of the noise strength and BM on the obtained W-shaped soliton. To determine the stability or instability zones, it was used the linear stability tool. It is shown that by varying the different parameters the Modulation bands can grow instability and stability zones can also emerge. These results permit to consolidate the previous works (Albosaily et al. in symmetry 12:1874, 2020, Abdelrahman et al. in AIMS Math 6:2970, 2021) exposed on the effects of noise on the soliton and the MI gain is new in this context. [ABSTRACT FROM AUTHOR]
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- 2022
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7. Specific optical solitons solutions to the coupled Radhakrishnan–Kundu–Lakshmanan model and modulation instability gain spectra in birefringent fibers.
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Abbagari, Souleymanou, Houwe, Alphonse, Doka, Serge Y., Inc, Mustafa, and Bouetou, Thomas B.
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BIREFRINGENT optical fibers , *BIREFRINGENCE , *OPTICAL solitons , *MATHEMATICAL transformations - Abstract
In this work, we examine optical solitons to the Radhakrishnan–Kundu–Lakshmanan equation (RKL) equation which describes the optical pulses in birefringent fiber (Raza and Javid in J Appl Anal Comput 10:1375–1395, 2020; Seadawy et al. in Opt Quant Electron 53:324, 2021) by using the New Generalized Auxiliary Equation Method (NGAEM). After some mathematical transformations, owing some constraint relations it is obtained two categories of soliton solutions. The first includes bright and dark optical solitons, while in the second class it is divulged the combined bright-dark and bright-bright optical solitons. Taking some suitable parameters of the model and the NGAEM, it is put up W-shaped optical solitons and diverse other solutions. Thereafter, we use the continuous waves as solutions of the model with small perturbations, to show the effects of the TOD, ellipticity angle and XPM on the Modulation Instability (MI) gain in normal and anomalous dispersion regime. It has been indicated that the third-order dispersion in normal/aanomalous dispersion regime can generate MI growth rate. At the same time, the ellipticity angle and such others parameters of the model play an important role during the MI growth rate (gain). Compared the obtained appropriate results in terms of analytical results and dynamics of the MI to Refs. (Raza and Javid 2020; Seadawy et al. 2021; Yepez-Martinez et al. in Chin J Phys 58:137–150, 2019; Drummond et al. in Opt Commun 78:137–142, 1990; Li et al. in Commun Theor Phys 65:231–236, 2016), they are new in our knowledge. [ABSTRACT FROM AUTHOR]
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- 2022
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8. W-shape bright and several other solutions to the (3+1)-dimensional nonlinear evolution equations.
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Saliou, Youssoufa, Abbagari, Souleymanou, Houwe, Alphonse, Osman, M. S., Yamigno, Doka Serge, Crépin, Kofané Timoléon, and Inc, Mustafa
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SCHRODINGER equation , *NONLINEAR waves , *PLASMA waves , *TRIGONOMETRIC functions , *NONLINEAR evolution equations - Abstract
By employing the Modified Sardar Sub-Equation Method (MSEM), several solitons such as W-shape bright, dark solitons, trigonometric function solutions and singular function solutions have been obtained in two famous nonlinear evolution equations which are used to describe waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in a plasma. These models are the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation, respectively. Comparing the obtained results with Refs. 32–34 and Refs. 43–46, additional soliton-like solutions have been retrieved and will be useful in future to explain the interaction between lower nonlinear ion-acoustic waves and the parameters of the MSEM and the obtained figures will have more physical explanation. [ABSTRACT FROM AUTHOR]
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- 2021
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9. Generalized Darboux transformation and higher-order rogue wave solutions to the Manakov system.
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Mukam, Serge P., Abbagari, Souleymanou, Houwe, Alphonse, Kuetche, Victor K., Inc, Mustafa, Doka, Serge Y., Bouetou, Thomas B., and Akinlar, Mehmet Ali
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ROGUE waves , *DARBOUX transformations , *NONLINEAR Schrodinger equation , *PHENOMENOLOGICAL theory (Physics) - Abstract
In this paper, we propose a recursive Darboux transformation in a generalized form of a focusing vector Nonlinear Schrödinger Equation (NLSE) known as the Manakov System. We apply this generalized recursive Darboux transformation to the Lax-pairs of this system in view of generating the Nth-order vector generalization rogue wave solutions with a rule of iteration. We discuss from first- to three-order vector generalizations of rogue wave solutions while illustrating these features with some 3D, 2D graphical depictions. We illustrate a clear connection between higher-order rogue wave solutions and their free parameters for better understanding the physical phenomena described by the Manakov system [ABSTRACT FROM AUTHOR]
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- 2021
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10. Optical soliton and weierstrass elliptic function management to parabolic law nonlinear directional couplers and modulation instability spectra.
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Houwe, Alphonse, Abbagari, Souleymanou, Nestor, Savaissou, Inc, Mustafa, Hashemi, Mir Sajjad, Betchewe, Gambo, and Doka, Serge Y.
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DIRECTIONAL couplers , *TRIGONOMETRIC functions , *OPTICAL fibers , *ELLIPTIC functions , *METAMATERIALS - Abstract
This paper shows out optical soliton solutions of the twin-core couplers with parabolic law nonlinearity with optical metamaterials parameters. It is used the improved new sub-ODE method (SOM) to found dark optical soliton, trigonometric function solutions, bright optical soliton and Jacobian elliptic function (JEF) solutions. Besides, physical explanation of the obtained bright and dark optical soliton solutions have been done and the influence of some parameters of the model have been set out. As the two-core coupler is favorable for modulation instability (MI), it has been studied the steady state of the results. More importantly, we have checked the effects of the optical metamaterials parameters on the formation of the Modulation bands in normal and anomalous dispersive regime. The results obtained in this paper set out Weierstrass Elliptic Function solutions compared to Mirzazadeh et al. (J Nonlinear Opt Phys Mater 24:1550017, 2015), Vega-Guzman et al. (Acta Phys Pol A 133:167–178, 2018) and will be helpful in the feature in optical birefringent fibers. [ABSTRACT FROM AUTHOR]
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- 2021
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11. Chirped solitary waves of the perturbed Chen–Lee–Liu equation and modulation instability in optical monomode fibres.
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Houwe, Alphonse, Abbagari, Souleymanou, Almohsen, Bandar, Betchewe, Gambo, Inc, Mustafa, and Doka, Serge Y.
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OPTICAL modulation , *GROUP velocity dispersion , *SELF-phase modulation , *FIBERS , *OPTICAL solitons - Abstract
In this paper, we show out the chirped and the corresponding chirp with their stability to the perturbed Chen–Lee–Liu equation with self-phase modulation and nonlinear dispersions. By employing the traveling-wave technique, we establish directly the nonlinear ordinary differential (NODE) equation. Based on the parameters of the obtained NODE, several cases of the exact traveling wave have been obtained with their corresponding chirp. We, also note that the group velocity dispersion, the self-phase modulation and the nonlinear dispersion terms have impacted the gain spectrum of the modulation instability (MI). The one important aspect is that without computer codes all these results were obtained. These results will be certainly helpful in optical fibers. [ABSTRACT FROM AUTHOR]
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- 2021
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12. Analytical survey of the predator–prey model with fractional derivative order.
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Abbagari, Souleymanou, Houwe, Alphonse, Saliou, Youssoufa, Douvagaï, Chu, Yu-Ming, Inc, Mustafa, Rezazadeh, Hadi, and Doka, Serge Y.
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NONLINEAR evolution equations , *NONLINEAR equations , *TRIGONOMETRIC functions , *LOTKA-Volterra equations , *HUMAN behavior models , *SOLITONS - Abstract
This work addresses the analytical investigation of the prey–predator behavior modeled by nonlinear evolution equation systems with fractional derivative order. Through the New Extended Algebraic Method (NEAM), we unearthed diverse types of soliton solutions including bright, dark solitons, combined trigonometric function solutions, and singular solutions. Besides the results obtained in the work of Khater, some new complex soliton solutions are also unearthed. The NEAM can also be used like the synthesis of the two mathematical tools. [ABSTRACT FROM AUTHOR]
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- 2021
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13. Modulation instability, bifurcation analysis and solitonic waves in nonlinear optical media with odd-order dispersion.
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Houwe, Alphonse, Abbagari, Souleymanou, Akinyemi, Lanre, Saliou, Youssoufa, Justin, Mibaile, and Yamigno Doka, Serge
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SOLITONS , *NONLINEAR waves , *GROUP velocity dispersion , *WAVE analysis , *DATA transmission systems , *NONLINEAR Schrodinger equation - Abstract
In this paper, modulation instability, bifurcation analysis, and soliton solutions are investigated in nonlinear media with odd-order dispersion terms. A generalized nonlinear Schrödinger equation with fourth-order dispersion and cubic-quintic nonlinearity is considered. A linear analysis method is used to derive an expression of the modulation instability spectrum, and the effects of the fourth-order and group velocity dispersion are pointed out on the modulation instability bands. The results show that for negative values of the fourth order in a normal dispersion regime, the modulation instability vanishes. Another important aspect is revealed when the fourth-order dispersion gets positive and has high values; additional bands emerge to enlarge the bandwidths of the modulation instability. To further confirm the effects of the odd-order dispersion in the nonlinear structure, the bifurcation, phase portraits, and chaotic behaviors have been investigated to show how instability arises in the nonlinear structure. Using numerical simulation, in particular the Runge-Kutta algorithm, the sensitivity of nonlinear systems is pointed out to confirm an unstable behavior. This investigation confirms once again the fact that the modulation spectrum is sensitive to higher-order dispersion in normal and anomalous dispersion regimes. A traveling wave hypothesis is employed to lead to the direct integration of the nonlinear system, and some specific soliton solutions are extracted. For particular constraint conditions on the discriminant, bright and dark solitons as well as Jacobi elliptic function solutions emerge. The obtained results could be used to improve the transmission signal via the optical fiber and secure the data in communication systems. • Modulation instability, bifurcation analysis, and soliton solutions are investigated in this paper. • A generalized nonlinear Schrodinger equation with quartic dispersion and cubic-quintic nonlinearity is considered. • The effects of the fourth-order and group velocity dispersion are pointed out on the modulation instability bands. [ABSTRACT FROM AUTHOR]
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- 2023
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14. Modulated wave patterns brought by higher-order dispersion and cubic–quintic nonlinearity in monoatomic chains with anharmonic potential.
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Abbagari, Souleymanou, Houwe, Alphonse, Akinyemi, Lanre, and Bouetou, Thomas Bouetou
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NONLINEAR Schrodinger equation , *MULTIPLE scale method , *WAVENUMBER , *SOLITONS , *SEPARATION of variables , *DISPERSION (Chemistry) - Abstract
This work investigates the modulation instability and wave patterns in the extended nonlinear Schrödinger equation with higher-order dispersion and cubic–quintic nonlinearity. We use the one-dimensional monoatomic chain with anharmonic potential to derive the discrete model. From the multiple scale method combined with a quasidiscreteness approximation, we derive the cubic–quintic nonlinear schrödinger equation, and thereafter an expression of the modulation instability gain is obtained by using a linearized expression. One notices that the modulation instability growth is sensitive to the higher-order dispersion and nonlinearities terms. A split-step Fourier method is used to assess the analytical predictions. A long evolution of the continuous wave is shown to lead to the formation of the bright soliton, and Akhemediev breathers also emerge to manifest the modulation instability. We have also demonstrated that the excitation wave number generates the train of waves to confirm the fact that the continuous wave can grow exponentially with any value of the latter. We mention equally that the model of the extended cubic–quintic nonlinearity with complex envelope has opened new features of the modulated wave patterns in monoatomic chains. • The MI and waves patterns of the NLSE are investigated. • To obtain CQ NLSE we use multiple scale method and quasi-discreteness approximation. • A split-step Fourier method is used to assess the analytical predictions. • Bright solitons and Akhemediev breathers also emerges to manifestthe MI. • The CW can grow exponentially with any value of the excitation wave number. [ABSTRACT FROM AUTHOR]
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- 2023
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15. Modulation instability gain and localized waves in the modified Frenkel–Kontorova model with high-order nonlinearities.
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Houwe, Alphonse, Abbagari, Souleymanou, Akinyemi, Lanre, Doka, Serge Yamigno, and Crépin, Kofané Timoléon
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ROGUE waves , *NONLINEAR evolution equations , *NUMERICAL integration , *SOLITONS - Abstract
In this paper, modulation instability and nonlinear supratransmission are investigated in a one-dimensional chain of atoms using cubic–quartic nonlinearity coefficients. As a result, we establish the discrete nonlinear evolution equation by using the multi-scale scheme. To compute the modulation instability gain, the linearizing technique is employed. The effect of the higher nonlinear component on modulation instability is particularly examined. Following that, full numerical integration was performed to identify modulated wave patterns as well as the appearance of a rogue wave. Through the nonlinear supratransmission phenomenon, one end of the discrete model is driven into the forbidden bandgap. As a consequence, for driving amplitudes above the supratransmission threshold, the bright soliton and modulated wave patterns are satisfied. An important behavior is observed in the transient range of time of propagation when the bright soliton wave turns into a chaotic soliton wave. These results corroborate our analytical investigations on the modulation instability and show that the one-dimensional chain of atoms is a fruitful medium to generate long-lived modulated waves. [ABSTRACT FROM AUTHOR]
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- 2023
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16. Modulation instability gain and nonlinear modes generation in discrete cubic-quintic nonlinear Schrödinger equation.
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Abbagari, Souleymanou, Houwe, Alphonse, Saliou, Youssoufa, Akinyemi, Lanre, Rezazadeh, Hadi, and Bouetou, Thomas Bouetou
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NONLINEAR Schrodinger equation , *NONLINEAR optics , *SCHRODINGER equation , *FIBER optics - Abstract
In this paper, we examined the effects of the nonlinear parameters and driven amplitude on the training envelope in discrete cubic-quintic nonlinear Schrödinger equation with arbitrarily high-order nonlinearities. From the numerical simulation, we exhibited the generation of the train of pulses and dark soliton when the driven amplitude is above the threshold. For a specific time of propagation, we illustrate how the variation of the driven amplitude and the nonlinear cubic-quintic parameters can generate instability in the forbidden gap. It emerges that the model of the discrete nonlinear Schrödinger equation with arbitrarily high-order nonlinearities can be used to generate the train of waves despite the fact that it is not integrable in the continuum limit approximation. We also displayed the effects of the cubic-quintic terms on the modulation instability growth rate. The obtained results will open new features to the train of pulses and dark soliton in the nonlinear fibers optics. • We studied discrete cubic-quintic nonlinear Schrödinger equation with arbitrarily high-order nonlinearities. • We examined the effects of the nonlinear parameters and driven amplitude on the training envelope in this nonlinear model. • We illustrated the effects of the cubic-quintic terms on the modulation instability growth rate. • The obtained solutions are depicted by 2D and 3D plots. [ABSTRACT FROM AUTHOR]
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- 2022
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17. Modulation instability gain and wave patterns in birefringent fibers induced by coupled nonlinear Schrödinger equation.
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Houwe, Alphonse, Abbagari, Souleymanou, Saliou, Youssoufa, Akinyemi, Lanre, and Doka, Serge Y.
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NONLINEAR Schrodinger equation , *GROUP velocity dispersion , *SOLITONS , *FOUR-wave mixing , *OPTICAL fibers , *FIBERS , *SCHRODINGER equation - Abstract
In this work, we studied the behavior of the modulation instability (MI) growth rate and modulated wave (MW) bright and dark-soliton in nonlinear optical fibers (OFs) where both birefringence and four-wave mixing (4WM) terms are employed. We have shown the effects of the 4WM and the group velocity dispersion (GVD) on the MI gain and MI bands as well as on the MWs patterns. For certain conditions on the coupled nonlinear Schrödinger equation (CNLSE) parameters, we exhibited stable and unstable zones of the MI. More precisely, in a normal dispersion regime, we shown how the variation of 4WM can generate additional sides lobes and consequently the formation of new MI bands. Furthermore, it is observed that when the coupling coefficient (CC) increases, its effects could reduce the stability zones by increasing strongly the number of sides lobes in a normal dispersion regime. To seek the behavior of the MWs patterns, we used numerical investigation (NI). From these results, it has been observed the propagation of the MW bright-soliton and dark-soliton with the effects of the 4WM. We noticed that the MWs patterns can preserve high energy on the peak and keep constant its shapes in birefringent OFs. These results show that the 4WM and the GVD behave as being energy sources for MI and MWs. Our finding can help to manufacture OF tools and could open the way for the use of the 4WM and cross-phase modulation (XPM) to generate MI bands and long-live temporal MWs patterns. • Modulation Instability. • Modulated wave pattern. • Cross-Phase Modulation. • Solitons. [ABSTRACT FROM AUTHOR]
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- 2023
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18. Modulated wave and modulation instability gain brought by the cross-phase modulation in birefringent fibers having anti-cubic nonlinearity.
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Abbagari, Souleymanou, Saliou, Youssoufa, Houwe, Alphonse, Akinyemi, Lanre, Inc, Mustafa, and Bouetou, Thomas B.
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ELLIPTIC functions , *FIBERS , *ENERGY conservation , *OPTICAL fibers , *NONLINEAR Schrodinger equation - Abstract
In this paper, we investigate the modulated wave and W-shaped profile in birefringent fibers having the anti-cubic nonlinearity terms. We use the traveling wave hypothesis to show out the velocity of the soliton and the constraint relation on the anti-cubic nonlinear terms. We use the Jacobi elliptic function solutions to point out two types of combined solutions. After some assumption on the modulus of the Jacobi elliptic function, we have shown out the combined bright-bright soliton and dark-dark soliton-like solutions. We use the linearizing algorithm to analyze the modulation instability (MI) growth rate. We have shown that the anti-cubic nonlinear terms and cross-phase modulation (XPM) can increase MI bands and the amplitude of the MI growth rate. To corroborate the prediction made on analytical results, we use the numerical investigation to show the propagation of the modulated wave and W-shaped profile in terms of cell index. We exhibited through the numerical results that the modulated wave can conserve high energy during its propagation in birefringent fibers. The obtained results will certainly open new perspectives in optical fibers during the transmission of huge data. • The modulated wave and W-shaped profile in birefringent fibers having the anti-cubic nonlinearity terms is studied. • The linear stability analysis is used. • The derived solutions are displayed using 2D and 3D plots. [ABSTRACT FROM AUTHOR]
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- 2022
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19. Rational W-shape solitons on a nonlinear electrical transmission line with Josephson junction.
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Halidou, Hamadou, Abbagari, Souleymanou, Houwe, Alphonse, Inc, Mustafa, and Thomas, Bouetou B.
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NONLINEAR Schrodinger equation , *ELECTRIC lines , *SOLITONS , *ROGUE waves , *JOSEPHSON junctions , *NONLINEAR waves , *SCHRODINGER equation - Abstract
• The nonlinear discrete equation is studied. • The rational w- shape solitons are retrieved. • The modulation analysis is presented. • The obtained solutions are presented by 2D and 3D figures. This paper examines envelope solitons, rational W-shape solitons to a Nonlinear Electrical Transmission Line (NETL) with Josephson junction (JJ) that consist of the N t h cells of circuits. By employing the reductive perturbation approach in the semi-discrete approximation, we obtain the nonlinear Schrödinger equation (NLSE). From this equation, the frequency ranges of propagation of bright and dark solitons were obtained. As in most of the works, the NLSE obtained is well known as the seat of rogue waves and Peregrine solitons. The nonlinearity provided by the JJ, combined with the dispersion, made it possible to study the Modulation Instability (MI) gain spectrum. The 3D and 2D graphical representations illustrated the instability zones and the W-rational solutions have followed by using numerical simulation. The results obtained in this paper are of a very capital contribution for the study of rogue waves in nonlinear transmission lines or other physical problems. [ABSTRACT FROM AUTHOR]
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- 2022
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20. Modulation instability gain and discrete soliton interaction in gyrotropic molecular chain.
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Abbagari, Souleymanou, Houwe, Alphonse, Akinyemi, Lanre, Saliou, Youssoufa, and Bouetou, Thomas Bouetou
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NONLINEAR Schrodinger equation , *MOLECULAR interactions , *SCHRODINGER equation , *NONLINEAR equations , *THEORY of wave motion , *SOLITONS - Abstract
In this paper, we considered a discrete coupled nonlinear Schrödinger equations (CNLSEs) which describes the propagation of solitonic waves in a gyrotropic molecular chain (GMC) of left and right circularly polarized intramolecular vibrations. From the linear analysis, we shown the forward and backward waves for left and right-handed modes. We underlined the effects of the gyrotropy term and effective mass (EM) on both modulation instability (MI) gain and modulated wave (MW) pattern. It reveals for strong enough values of these parameters that the generation of new sides lobes and MI bands. For numerical simulation, we shown out the propagation and interaction of the MW bright-soliton with high energy on the peak. It results from this investigation that gyrotropy term and EM behave as being energy sources in GMC. Finally, the reported outcomes can be used during the transfer of energy in molecular chain. • We studied discrete coupled nonlinear Schrodinger equations. • These equations describe the propagation of solitonic waves in a gyrotropic molecular chain. • We exhibited the discrete solitons interaction in the gyrotropic molecular chain • We investigated the effects of gyrotropy term and effective mass on the modulated waves. • The linear analysis and modulation instability are provided. [ABSTRACT FROM AUTHOR]
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- 2022
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21. W-shaped profile and multiple optical soliton structure of the coupled nonlinear Schrödinger equation with the four-wave mixing term and modulation instability spectrum.
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Abbagari, Souleymanou, Houwe, Alphonse, Doka, Serge Y., Bouetou, Thomas B., Inc, Mustafa, and Crepin, Kofane T.
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FOUR-wave mixing , *NONLINEAR Schrodinger equation , *SCHRODINGER equation , *SOLITONS , *KERR electro-optical effect , *OPTICAL solitons , *DATA transmission systems , *LINEAR statistical models - Abstract
• The Coupled Nonlinear Schrödinger Equation (CNLSE) throughout Kerr law nonlinearity is considered. • The linear stability analysis is used. • The modulation instability analysis is presented. • The obtained results are showed by 2D and 3D Figures. We investigate diverse optical solitons and other solution for the Coupled Nonlinear Schrödinger Equation (CNLSE) having Four-Wave Mixing (FWM) and Kerr nonlinearity term. We stress the effects of different parameters of the model on the obtained optical soliton by employing the New Generalized Extended Direct Algebraic Method (NGEDAM). The solutions contain W-shaped profile of the bright optical soliton, dark optical soliton and diverse other solutions including the combined complex optical soliton. Interestingly, W-shaped optical soliton and dark optical soliton own a good argument for long communication and big data transmission originating from the self-steepening, Kerr nonlinearity effects and FWM. We also, emphasize the Modulation Instability (MI) gain spectra to narrow the impact of the FWM in birefringence. Thereafter, we involve the ellipticity angle effects in normal and anomalous dispersion regime on the MI gain spectra. Parametric conditions for the existence of the obtained optical soliton solutions and MI gain are given. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
22. Modulated waves patterns in the photovoltaic photorefractive crystal.
- Author
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Dikwa, Jérôme, Houwe, Alphonse, Abbagari, Souleymanou, Akinyemi, Lanre, and Inc, Mustafa
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NONLINEAR Schrodinger equation , *SCHRODINGER equation , *SOLITONS , *SHORT circuits , *CRYSTALS , *THEORY of wave motion , *INDUCTIVE effect - Abstract
In this paper, we investigated the propagation of the modulated waves (MWs) patterns with the effects of the external field (EF) in a photorefractive crystal. To do so, we use the coupled nonlinear Schrödinger equations and we apply the auxiliary equation method to point out four families of solutions such as bright, dark, combined bright-dark, and bright-bright soliton. We pointed out the effects of EF on the modulation instability growth rate. Throughout the numerical simulation, we show that EF can generate MWs patterns when the short and open circuit condition is considered in the case of bright soliton. However, when we consider dark soliton solution as an initial condition and we have only obtained the MW pattern in the case of a short circuit. It results in this study of the propagation of the MWs patterns and chaos-like motion for specific cell indexes. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
23. Envelope solitons of the nonlinear discrete vertical dust grain oscillation in dusty plasma crystals.
- Author
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Houwe, Alphonse, Abbagari, Souleymanou, Inc, Mustafa, Betchewe, Gambo, Doka, Serge Y., and Crépin, Kofane T.
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- *
DUSTY plasmas , *MODULATIONAL instability , *OPTICAL solitons , *PLASMA oscillations , *NONLINEAR Schrodinger equation , *DUST , *SOLITONS - Abstract
• The vertical grain displacement model is presented. • The acquired results are given by some figures. • The modulation analysis is given. • Bright, dark and singular optical solitons are presented. The paper concerns envelope soliton propagating through the nonlinear transverse dust grain displacement in dusty plasma crystals. The work found its motivation from the recent paper of the authors [7]. To reach the goal of this study we establish the linear dispersion and the nonlinear Schrödinger equation (NLSE) by employing the quasi discrete approximation [7,13–15]. Contrary to ref. [7] , it is observed one additional regime of the formation of the dark soliton while choosing the gap frequency value (ω g ≈ 150 sec −) which is close to the experimental value given by Motcheyo et al. [7] , Tsopgue et al. To corroborate the prediction made analytically to group velocity, was confirmed by numerical and experimental studies. As, it is established that in general manner the modulated waves describing by the NLSE can be stable or unstable to the perturbation, the modulation instability of steady state have been done. Despite, that the bandwidth of the model has been reduced compared to [7,13–15] , we can say without hesitation that this work will be a capital contribution in dusty plasma crystal. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
24. Generalized stochastic Korteweg-de Vries equations, their Painlevé integrability, N-soliton and other solutions.
- Author
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Akpan, Udoh, Akinyemi, Lanre, Ntiamoah, Daniel, Houwe, Alphonse, and Abbagari, Souleymanou
- Subjects
- *
KORTEWEG-de Vries equation , *SOLITONS , *HYPERBOLIC functions , *SYMBOLIC computation - Abstract
In this study, we study two generalized stochastic Korteweg-de Vries (KdV) equations. The Painlevé property of these nonlinear models is tested using Kruksal's method, which establishes the model's integrability. As a result, using Hirota's bilinear approach and symbolic computation, the N-soliton solutions are constructed. In addition, the extended hyperbolic function method (EHFM), the modified Kudryashov method (MKM), and the sub-equation method (SEM) are used to acquire the bright soliton, dark soliton, singular soliton, periodic, rational, and exponential solutions. To help understand the dynamic features of the derived soliton solutions, we present a number of 2D, 3D, and contour graphs using appropriate parametric values. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Clout of fractional time order and magnetic coupling coefficients on the soliton and modulation instability gain in the Heisenberg ferromagnetic spin chain.
- Author
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Houwe, Alphonse, Abbagari, Souleymanou, Doka, Serge Yamigno, Inc, Mustafa, and Bouetou, Thomas B.
- Subjects
- *
OPTICAL solitons , *NONLINEAR waves , *SOLITONS , *THEORY of wave motion , *PEDESTALS - Abstract
• The Heisenberg ferromagnetic spin chain is studied. • The bright, dark, combined and rational optical solitons are constructed. • The modulation instability analysis is presented. • The obtained solutions are presented by 2D and 3D figures. In this paper we utilize the auxiliary equation method to show the leverage of the fractional derivative parameter and the Magnetic Coupling Coefficients (MCC) on the procured soliton solutions and the Modulation Instability (MI) gain in Heisenberg ferromagnetic spin. The pedestal of the work is set on the (2 + 1)-fractional time order dimensional Heisenberg ferromagnetic spin chain equation which demonstrate the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The results collected have enclosed bright-dark soliton, dark soliton and rational solutions. Compared the acquired results with Zhao et al. (2016) [26], Akbar (2021) [27], Hosseini et al. (2021b) [28], further soliton-like solutions have been drop in and the marvel of the fractional parameter has been exposed across the spatiotemporal and plot evolution of the bright and dark soliton solutions. Therewith, the MI bands have been stressed and it is observed some new attitude of the MI gain spectra under the induction of the MCC jointed with the fractional time derivative order. The collected results are new in literature in our knowledge and will give the pipe to the solitary waves theory in Heisenberg ferromagnetic spin including inhomogeneity parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
26. A study of (2+1)-dimensional variable coefficients equation: Its oceanic solitons and localized wave solutions.
- Author
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Akinyemi, Lanre, Manukure, Solomon, Houwe, Alphonse, and Abbagari, Souleymanou
- Subjects
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WAVES (Fluid mechanics) , *WATER waves , *FLUID dynamics , *MARINE engineering , *NONLINEAR equations , *SOLITONS , *WATER depth - Abstract
In this work, shallow ocean-wave soliton, breather, and lump wave solutions, as well as the characteristics of interaction between the soliton and lump wave in a multi-dimensional nonlinear integrable equation with time-variable coefficients, are investigated. The Painlevé analysis is used to verify the integrability of this model. Based on the bilinear form of this model, we use the simplified Hirota's method obtained from the perturbation approach and various auxiliary functions to construct the aforementioned solutions. Besides, the interaction between the soliton and lump wave solutions is also examined. In addition, by imposing specific constraint conditions on the N-soliton solutions, we further derive higher-order breather solutions. To show the physical characteristics of this model, several graphical representations of the discovered solutions are established. These graphs show that the time-variable coefficients result in a variety of novel dynamic behaviors that differ significantly from those for integrable equations with constant coefficients. The acquired results are useful for the study of shallow water waves in fluid dynamics, marine engineering, nonlinear sciences, and ocean physics. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. Effects of the higher-order dispersion on solitary waves and modulation instability in a monomode fiber.
- Author
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Akinyemi, Lanre, Houwe, Alphonse, Abbagari, Souleymanou, Wazwaz, Abdul-Majid, Alshehri, Hashim M., and Osman, M.S.
- Subjects
- *
NONLINEAR Schrodinger equation , *OPTICAL solitons , *SEPARATION of variables , *NONLINEAR waves , *DISPERSION (Chemistry) - Abstract
In this paper, we investigate the modulation instability and the dynamics of solitary waves in a higher-order nonlinear Schrödinger equation. We use a powerful and robust method known as the modified sub-equation method to secure the solitary waves and other numerous solutions to this nonlinear model. Several constraint conditions that guarantee the existence of these solutions are highlighted. Utilizing a linearizing technique, we establish the modulation instability gain. The influence of the higher nonlinear component on the modulation instability is also discussed. Furthermore, we perform the numerical simulations of this model by using the split-step Fourier method. Finally, several solutions are shown in two and three dimensions to better explain the behavior of the considered model. The two-dimensional plots depict Peregrine soliton under the influence of the nonlinear dispersion term. These graphs are useful for understanding the dynamic properties of the obtained results. • New optical solitons for the HNSE were constructed. • The obtained solutions were found using the modified sub-equation technique. • The model's modulation instability is studied. • The physical meaning for the solutions is graphically investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
28. Discrete solitons in nonlinear optomechanical array.
- Author
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Alphonse, Houwe, Djorwe, Philippe, Abbagari, Souleymanou, Doka, Serge Yamigno, and Nana Engo, S.G.
- Subjects
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MODULATIONAL instability , *THEORY of wave motion , *INFORMATION processing - Abstract
The detection of the solitons whose the propagation is spatially localized on the array is an interesting feature for experimental purposes. Here, we investigate the effect of position-modulated self-Kerr nonlinearity on discrete soliton propagating in an optomechanical array. The optomechanical cells are coupled to their neighbors by optical channels, and each cell supports the self-Kerr nonlinear term. Modulational Instability (MI) together with numerical simulations are carried out to characterize the behavior of the solitonic waves. It results that the nonlinear term shortens the transient regime of the temporal solitonic waves, which allows the wave propagation to be confined along specific cells. As the nonlinear term increases, the pulsed shape of soliton waves get sharped and highly peaked. For a strong enough value of the nonlinear term, the waves feature chaos-like motion. Owing to these results, the position-modulated self-Kerr nonlinear term manifests itself as being an energy source for the solitonic waves, allowing to the generated solitons to propagate during a long time while acquiring energy. These results shed light on the fact that nonlinear optomechanical platforms could be used to generate long-lived temporal localized solitons and even chaotic solitonic waves, which are good prerequisites for information processing purposes. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
29. New optical solitons of nonlinear conformable fractional Schrödinger-Hirota equation.
- Author
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Rezazadeh, Hadi, Mirhosseini-Alizamini, Seyed Mehdi, Eslami, Mostafa, Rezazadeh, Mohammadreza, Mirzazadeh, Mohammad, and Abbagari, Souleymanou
- Subjects
- *
OPTICAL solitons , *NONLINEAR optics , *PARTIAL differential equations , *THEORY of wave motion , *MECHANICS (Physics) - Abstract
In this article, an amelioration of the approaches namely the new extended direct algebraic method for solving the nonlinear conformable fractional Schrödinger-Hirota equation (FSHE) is presented. By using the traveling wave transformation change the fractional equation into the ordinary differential equation, and with the aid of mathematical software Maple, a number of new optical solitons solutions for them are calculated. The obtained results show that the proposed method is powerful, effective, and straightforward technique to work out new solutions of various types of nonlinear fractional partial differential equations in applied sciences. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
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