Search

The purpose of this study is to introduce the wave structures and dynamical features of the third-order nonlinear Schrödinger equations (TONLSE). We take the original equation and, using the traveling wave transformation, convert it into the appropriate traveling wave system, from which we create a conserved quantity known as the Hamiltonian. The Jacobian elliptic function solution (JEF), the hyperbolic function solution, and the trigonometric function solution are just a few of the optical soliton solutions to the equation that may be found using the complete discrimination system (CDS) of polynomial method (CDSPM) and also transfer the JEF into solitary wave (SW) soltions. It also includes certain dynamic results, such as bifurcation points and critical conditions for solutions, that might be utilized to explore the dynamic features of the equation employing the CDSPM. This method could also be used for qualitative analysis. The qualitative analysis is used to illustrate the equilibrium points and phase potraits of the equation. Phase portraits are visual representations used in dynamical systems to illustrate a system's behaviour through time. They can provide crucial information about a system's stability, periodic behaviour, and the presence of attractors or repellents. [ABSTRACT FROM AUTHOR]

Lump and their interactions with kink, periodic and rogue waves, and periodic cross lump waves will be studied for fifth-order variable coefficient nonlinear-Schrödinger equation in this paper. With the combinations of bilinear, exponent, and trigonometric functions, we'll study different lump soliton solutions. With interaction phenomenon we'll set up some new analytical solutions and also represents them in graphical ways. [ABSTRACT FROM AUTHOR]

In this paper, we study chirp-free solitons (dromions) for the higher-order nonlinear Schrödinger equation (HNLSE) having non-Kerr terms with the aid of sub-ODE scheme. We find bright and singular dromion with domain walls, rational and periodic solitons, Weierstrass elliptic functions (WEFs), Jacobi elliptic solutions (JESs) and other solitary wave solutions for our governing model. The Sub-ODE scheme is very useful scheme, providing so many new solitary wave solutions especially JES and WEF solutions. We will also construct graphs of our results in different dimensions along with constraint conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study different analytical solutions for long water-wave equation (LWWE) like lump, breathers, rogue waves, periodic cross-kink, periodic wave, lump with one and two-kink, multiwave and periodic-cross lump. We compute the essential relationship between interaction between lump periodic and kink wave, periodic cross-kink and other types of exact solutions by studying the unknown nonlinear evolution equations (NLEEs) for long water wave. We show the graphical representation for our retrieve analytical solutions to observe the behavior of effective waves. [ABSTRACT FROM AUTHOR]

In this article, we construct multi-wave, homoclinic breather, M-shaped rational and periodic cross kink wave solutions for coupled-Higgs equation (CHE) by using distinct transformations. We obtain these solutions with the aid of logarithmic transformations and symbolic computations. Moreover, we also derive some soliton wave solutions for CHE in polynomial forms. These solutions include solitary wave, soliton wave and Jacobi elliptic function solutions and are found by implementing unified technique. We will also discuss the graphical structure of our newly achieved results. [ABSTRACT FROM AUTHOR]

This paper studies Attilio Maccari (AM) system for some new solitary wave solutions. We used sub-ODE scheme to find kink shape, bell type, Weierstrass and Jacobi elliptic, hyperbolic, periodic and other solitary wave solutions under some constraint conditions. We will also present our results graphically in distinct dimensions. [ABSTRACT FROM AUTHOR]

This paper retrives hyperbolic, periodic, singular, domain walls, dark-like dromions (solitons) for perturbed fractional nonlinear Schrödinger equation. We use a quite new technique known as extended modified auxiliary equation mapping method. This method is quite effective and delivers so many new dromions. We used conformable derivatives for our perturbed fractional NLSE with some constraint conditions. [ABSTRACT FROM AUTHOR]

In this paper, we will obtain lump-soliton solution for (1 + 1)-dimensional generalized hyperelastic rod equation, also known as generalized KdV equation by aid of Hirota bilinear method (HBM). We also obtain lump-multisoliton (which is an interaction of lump with one kink or two kink soliton) and lump-periodic solutions (which is formed by an interaction between lump and periodic waves). The dynamics of these solution are examined graphically by selecting significant parameters. [ABSTRACT FROM AUTHOR]

This work addresses the four main inducements: Lump, rogue wave, Homoclinic breather and multi-wave solutions for (2+1)-Modified Veronese Web (MVW) equation via Hirota bilinear approach and the ansatz technique. This model is a linearly degenerate integrable nonlinear partial differential equation (NLPDE) and can also be used to admit a differential covering with nonremoval physical parameters. By assuming the function f in the Hirota bilinear form of the presented model as the general quadratic function, trigonometric function and exponential function form, also with appropriate set of parameters, we have prevented the lump, rogue wave, breather and multi-wave solutions successfully. A precise compatible wave transformation is utilized to obtain multi-wave solutions of governing model. Also, the motion track of the lump, Rogue wave and multi-waves is also explained both physically and theoretically. These new results contain some special arbitrary constants that can be useful to spell out diversity in qualitative features of wave phenomena. [ABSTRACT FROM AUTHOR]

In this paper, we investigate resonanat nonlinear Schrödinger equation (RNLSE) with self steeping phenomena to obtain some chirped periodic (CP) and soliton waves. A chirp is a signal in which the frequency increases (up chirp) or decreases (down-chirp) with time. It is commonly used in sonar, radar and laser systems and in other applications, such as in spread-spectrum communications. We obtain chirped periodic waves (CPW) with some Jacobi elliptic functions (JEF). We also obtain some solitary waves (SW) like dark, bright, singular waves of type I and II, hyperbolic, periodic and other solutions. The dynamical behaviour for these waves will also be presented. [ABSTRACT FROM AUTHOR]

In this work, we retrieve a series of new wave solutions of the double dispersive equation that describes the nonlinear wave propagation in the elastic inhomogeneous Murnaghan's rod by applying a novel integration norm known as the Sardar sub-equation method (SSEM). The solutions recovered by this method can be categorized as topological, non-topological, combo topological–non-topological, periodic and mixed periodic, singular and mixed singular solutions. In addition, by allotting different values to parameters, the physical movements of attained solutions are shown by plotting the 3D, 2D and contour graphs. On the basis of achieved results, we may claim that the proposed computational method is direct, dynamics, well organized, and will be useful for solving the more complicated nonlinear problems in diverse areas together with symbolic computations, especially in engineering and applied sciences. [ABSTRACT FROM AUTHOR]

In this article, some novel optical and periodic wave structures are studied to the fractional Schrödinger–Hirota equation with a truncated M -fractional derivative. For this purpose, the integration scheme, which was adopted is fractional extended Fan sub-equation. The optical solitons are observed in single and combined forms, and some other solutions are also fall out during the derivation. Subsequently, the exact solutions demonstrate the effectiveness, efficiency and reliability of the proposed methods, which can be useful for exploring various kind of solutions in the diverse fields of contemporary sciences and engineering. The constraint conditions are utilized, as well as the gained solutions are plugged into the model to verify the results. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate a famous model of nonlinear sciences namely (2 + 1) -dimensional nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) model for the evaluation of optical travelling waves by implementing unified method (UM). We will extract dark as well as bright solitary waves along with elliptic waves. We will draw conserved quantities of our governing model by utilizing dilation symmetry. At the end, the integrability of nonlinear spin dynamics of HFSC model with the help of Painlevé test will also be studied in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we will find the chirped solitons (CS) solutions to the nonlinear schrödinger's equation (NLSE) under polynomial nonlinearity with spatio temporal dispersion (STD) and group velocity dispersion (GVD). We will find CS with Jacobi elliptic functions (JEF). We will also get some new solitary waves (SW) like bright, dark, kink, periodic, hyperbolic, and other solutions. The dynamical behaviour for these waves will also be discussed along with constraint conditions. [ABSTRACT FROM AUTHOR]

The focus of this article is to find some new exact solutions to the (2+1)-dimensional nonlinear Schrödinger equation (NLSE) with Kerr media by employing the auxiliary equation method. A set of novel travelling wave solutions are observed such as bright, dark, periodic and optical solitons (dromions). Moreover, the physical interpretation of nonlinear waves would also be demonstrated with the aid of scientific computing. [ABSTRACT FROM AUTHOR]

This paper studies the exact traveling wave solutions to the nonlinear Dullin–Gottwald–Holm model which has the application in shallow-water waves in which the fractional derivative is considered in the sense of conformable derivative. Diverse exact solutions in hyperbolic, trigonometric and plane wave forms are obtained using two integration norms. For this purpose G ′ / G -expansion method and reccati mapping techniques are used. The 3D plots and their corresponding contour graphs are also depicted. Being concise and straightforward, the calculations demonstrate the effectiveness and convenience of the method for solving other nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

Ternary alloys of Fe are very important materials having good corrosion resistance and are also famous for several high-temperature applications. The dynamical behavior of exact traveling waves for the kinetics of phase separation in Fe–Cr–X (X = Mo, Cu) ternary alloys is modelled by convective-diffusive Cahn–Hilliard (CH) equation. A variety of nonlinear dynamical exact and solitary wave structures are extracted in several forms like rational, hyperbolic, trigonometric function solutions by the utilization of a sound computational integration tool, i.e., Φ 6 -model expansion method. Besides, we also secure mixed combined solitons and singular periodic wave solutions with unknown parameters. Moreover, the constraint conditions observed during derivation lead to substantial solutions. The findings elucidate that the governing model theoretically possesses significantly rich structures of exact traveling wave solutions. Hence, our technique via fortification of symbolic computations provides an active and potent mathematical implementation for solving diverse benevolent nonlinear wave problems. [ABSTRACT FROM AUTHOR]

In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan–Kundu–Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations [ABSTRACT FROM AUTHOR]

In this study, we extract the different kinds of exact wave solutions to the (1+1) dimensional Chiral nonlinear Schrödinger equation (CNLSE) that describes the edge states of the fractional quantum hall effect in quantum field theory. The extended rational sine–cosine/sinh–cosh techniques are utilized for obtaining solutions. Parametric conditions on physical parameters are also enumerated to ensure the existence criteria of soliton solutions. Moreover, the stability analysis is also discussed. By the suitable selection of parameters, three dimensional, two dimensional and contour plots are sketched. The obtained outcomes show that the applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. [ABSTRACT FROM AUTHOR]

A particular attention is paid to the nonlinear dynamical exact wave solutions to the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation (DJKME). A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing ( G ′ G 2 ) -expansion function method and modified direct algebraic method. In addition, we also secure singular periodic and plane wave solutions with arbitrary parameters. We also discussed the modulation instability analysis of the governing model. The constraint conditions for the validity of existence of solutions are also reported. Moreover, three-dimensional and two-dimensional, and their corresponding contour graphs are sketched for a better understanding of the derived solutions with the values of arbitrary parameters. [ABSTRACT FROM AUTHOR]

The article investigates optical soliton to Radhakrishnan–Kundu–Lakshmanan (RKL) equation in birefringent fibers which involving two component form for vector solitons in telecommunication system. The optical solitons in the form of single and combined form like bright-dark, dark-singular, complex soliton and multiple solitons are extracted successfully by the mechanism of Fan-extended sub equation (FESE) approach with the effect of five free parameters. Moreover, we get singular periodic wave solutions and some constraint conditions for the existence of soliton and other solutions are also observed. Furthermore, by selecting the appropriate choices of the parameters 3D, 2D and corresponding contour graphs are presented to explain the results physically. The obtained outcomes show that the applied method is concise, direct, efficient and can be imposed in more complex phenomena with the assistant of symbolic computation to get variety of solitons by a single approach. [ABSTRACT FROM AUTHOR]

The focus of this article is to find some new exact solutions to the M-fractional paraxial nonlinear Schrödinger equation with Kerr media by employing the modified simple equation method and the auxiliary equation method. A set of novel travelling wave solutions are observed such as bright, dark, periodic and optical solitons. Moreover, the physical interpretation of nonlinear waves would also be demonstrated with the aid of scientific computing. [ABSTRACT FROM AUTHOR]

This article possesses modulation instability (MI) analysis and new exact wave solutions to unidirectional Dullin–Gottwald–Holm (DGH) system that describes the prorogation of waves in shallow water. The exact wave solutions in single and combined form like shock, singular, and shock‐singular are extracted by means of an innovative integration norm, namely, G′/G2‐expansion scheme. The periodic and plane wave solutions are also emerged. The constraint conditions which ensure the existence of solutions are discussed as well. Moreover, the choice of suitable parameters gives the three‐dimensional and two‐dimensional sketches, and furthermore, their contour plots are also drawn. [ABSTRACT FROM AUTHOR]

This paper studies the new closed form solutions to (2+1)-dimensional Bogoyavlenskii system that describes interaction of a Riemann wave propagation. The extended Fan sub-equation technique is used to investigate some new traveling wave solutions to the higher-dimensional coupled model. The obtained closed form solutions are named as shock, kink, shock and periodic soliton solutions. Clearly, the outcomes of the study confirm the strength of the current approach. Moreover, the obtained results are helpful for the understanding of non-linear wave propagation and are of great interest to present-day scientists and can be employed to deal with more complex models arising in diverse disciplines of contemporary science. [ABSTRACT FROM AUTHOR]

In this article, we investigate the optical soiltons and other solutions to Kudryashov's equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as Φ 6 -model expansion method. Singular periodic wave solutions are recovered and the constraint conditions, which provide the guarantee to the soliton solutions are also reported. Moreover, modulation instability (MI) analysis of the governing equation is also discussed. By selecting the appropriate choices of the parameters, 3D, 2D, and contour graphs and gain spectrum for the MI analysis are sketched. The obtained outcomes show that the applied method is concise, direct, elementary, and can be imposed in more complex phenomena with the assistant of symbolic computations. [ABSTRACT FROM AUTHOR]

We successfully apply extended rational sine-cosine/sinh-cosh and advance expansion function techniques in this paper. Various kinds of soliton solutions to the conformable time-fractional resonant nonlinear Schrödinger equation (RNLSE) in optical fiber are extracted. We discuss the system with the effects of coefficients like group velocity dispersion, non-Kerr nonlinearity, resonant nonlinearity, and construct optical soliton solution in terms of rational, trigonometric and hyperbolic function solutions with arbitrary parameters. The recovered solutions reveal that the applied approaches are straightforward and efficient to work out the excellent contribution for analyzing several classes of nonlinear partial differential equations (NLPDEs) in engineering and sciences. Moreover, 3D, 2D and contour graphs are sketched with suitable selection of the parameters under the criteria of constraints conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the new solitons and closed form solutions to (3 + 1) dimensional resonant nonlinear Schrödinger equation (RNLSE) that explains the behavior of waves with the effect of group velocity dispersion and resonant nonlinearities in the optical fiber. The soliton solutions in single and combined forms like dark, singular, and dark-singular in mixed form are extracted by means of two innovative integration norms namely extended sinh-Gordon equation expansion and ( G ′ G 2 ) -expansion function methods. Moreover, kink and closed form solutions are also observed under different constraint conditions. By choosing the suitable selection of the parameters, three dimensional, two dimensional, and contour plots are sketched. The obtained outcomes show that the applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. [ABSTRACT FROM AUTHOR]

The paper studies the single and combined optical solitons in the physical model of telecommunication system that describes the dynamics of optical solitons with quadratic–cubic nonlinearity in the mitigate internet bottleneck. This fractional temporal evolution is considerd with the coefficients of self-steeping, group velocity, inter-model and nonlinear dispersions. The extended Fan sub-equation method is used to investigate the families of single optical solitons (bright, dark and singular) for the different values of parameters. [ABSTRACT FROM AUTHOR]

In this article, some new traveling wave solutions to the space-time fractional equal-width equation are constructed with the help of the extended Fan sub-equation method. A simple transformation is introduced to convert the fractional order partial differential equation into an ordinary differential equation. As a result, the bright, dark, singular and combined wave solitons are observed for different values of two parameters. Moreover, the graphical representations are also depicted. [ABSTRACT FROM AUTHOR]