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This work is on the retrieval of quiescent optical solitons for the complex Ginzburg–Landau equation that is with nonlinear chromatic dispersion and generalized structure of quadratic–cubic form of self–phase modulation. The Lie symmetry is applied to make this retrieval possible. The model is studied with linear temporal evolutions as well as generalized temporal evolution. [ABSTRACT FROM AUTHOR]

The current paper extracts the implicit form of quiescent optical solitons that emerge from the nonlinear Schrödinger’s equation with the generalized form of quadratic–cubic nonlinear refractive index change. The work is with linear temporal evolution as well as with generalized temporal evolution. The results are in terms of Appell hypergeometric functions as in the case of the quadratic–cubic form of nonlinear refractive index, reported earlier. Lie symmetry analysis has made this retrieval possible. [ABSTRACT FROM AUTHOR]

This paper addresses Radhakrishnan--Kundu--Lakshmanan equation that arises in the study of soliton dynamics in optical fibers. The bifurcation analysis is carried out and the phase portraits are displayed. The complete discriminant analysis also leads to solitons and other solutions to the model. [ABSTRACT FROM AUTHOR]

In this paper, highly dispersive optical solitons are obtained with the perturbed complex Ginzburg--Landau equation, incorporating the Kerr law of nonlinearity, by the complete discriminant classification approach. A variety of solutions emerge from this scheme that include solitons, periodic solutions and doubly periodic solutions. The numerical sketches support the analytical findings. [ABSTRACT FROM AUTHOR]

This work recovers optical soliton solutions to the concatenation model with differential group delay in the presence of white noise along both the components. Two integration algorithms have successfully recovered a full spectrum of solitons solutions to the model. It has been proved that the effect of white noise is visible only in the phase portion of the solitons along both components. [ABSTRACT FROM AUTHOR]

This work numerically studies bright and dark optical solitons that emerge from the dispersive concatenation model, having the Kerr law of nonlinear refractive index, using the Laplace-Adomian decomposition scheme. The simulations, surface plots, and contour plots are presented. The error measure is observed to be infinitesimally small. [ABSTRACT FROM AUTHOR]

This paper retrieves numerically the bright and dark 1-soliton solutions for the newly constructed concatenation model using the Laplace-Adomian decomposition technique. The errors analysis is also conducted, and they are of the order of 10-9. The surface, sectional, and error plots are exhibited for bright and dark solitons. [ABSTRACT FROM AUTHOR]

In the current paper, a full spectrum of 1-soliton solutions to the concatenation model with the power-law of self-phase modulation has been recovered. The method of undetermined coefficients has permitted us to solve this problem successfully. The parameter constraints naturally emerge from the derivation and are also listed, guaranteeing these solitons' existence. It has been proved that dark solitons and singular solitons of a specific type would exist only when the power-law parameter collapses to unity. [ABSTRACT FROM AUTHOR]

This paper presents optical solitons with the concatenation model having spatio-temporal and chromatic dispersions. This model can advantageously curtail the Internet bottleneck effect. Two integration schemes yield these solitons. By utilizing the multipliers approach, the conservation laws are also derived. [ABSTRACT FROM AUTHOR]

In the current study, the concatenation model of birefringent fibers is explored for the first time, and we present optical soliton solutions to the model. The integration algorithm used to achieve this retrieval is the method of undetermined coefficients, which yields a wide range of soliton solutions. The parameter constraints arise naturally during the derivation of the soliton solutions, which are essential for such solitons to exist. [ABSTRACT FROM AUTHOR]

This paper recovers quiescent optical solitons that are self-sustaining, localized wave packets that maintain their shape and amplitude over long distances due to a balance between nonlinearity and dispersion. When a soliton is in a state of quiescence, it means that it is stationary in both space and time. Quiescent optical solitons are typically observed in optical fibers, where nonlinearity and dispersion can lead to the formation of solitons. The concatenation model is considered to understand the behavior of optical pulses propagating through nonlinear media. Here, we consider the familiar nonlinear Schrödinger equation, the Lakshmanan–Porsezian–Daniel equation, and the Sasa–Satsuma equation. The current paper also addresses the model with nonlinear chromatic dispersion, a phenomenon that occurs in optical fibers and other dispersive media, where the chromatic dispersion of the material is modified by nonlinear effects. In the presence of nonlinearities, such as self-phase modulation and cross-phase modulation, the chromatic dispersion coefficient becomes a function of the optical intensity, resulting in nonlinear chromatic dispersion. A full spectrum of stationary optical solitons, along with straddled stationary solitons, are obtained. There are four integration schemes that made this retrieval possible. The numerical simulations are also included for these solitons. The parameter constraints also indicate the existence criteria for these quiescent solitons. [ABSTRACT FROM AUTHOR]

We derive stationary optical solitons for the case when the nonlinear refractive index of Kudryashov's quintuple form is coupled with a nonlocal type of self-phase modulation in the presence of nonlinear chromatic dispersion. An enhanced Kudryashov's approach has made this derivation of soliton solutions possible for the case of generalized temporal evolution. [ABSTRACT FROM AUTHOR]

This work is a sequel to the previously reported results on stationary optical solitons with several forms of Kudryashov's law of self-phase modulation. The study is conducted with generalized temporal evolution by the aid of extended trial function approach. The solutions that naturally emerged from this scheme are in terms of Jacobi's elliptic function which finally led to stationary solitons with the modulus of ellipticity approaching its appropriate limit. [ABSTRACT FROM AUTHOR]

The paper concentrates on the solitary waves that are retrievable from the generalized Boussinesq equation. The numerical simulations are displayed in the paper that gives a visual perspective to the model studied in neurosciences. The Laplace–Adomian decomposition scheme makes this visualization of the solitons possible. The numerical simulations are being reported for the first time using an elegant approach. The results would be helpful for neuroscientists and clinical studies in Medicine. The novelty lies in the modeling that is successfully conducted with an impressively small error measure. In the past, the model was integrated analytically only to recover soliton solutions and its conserved quantities. [ABSTRACT FROM AUTHOR]

This paper secures solitary waves, shock waves and singular solitary waves for the Boussinesq equation, which is studied with the inclusion of surface tension. The method of undetermined coefficients has yielded such waves. The Lie symmetry analysis has introduced a fresh perspective to the model. Conserved densities and corresponding conserved quantities are computed using the multiplier approach. [ABSTRACT FROM AUTHOR]

This paper studies dispersive bright and dark optical solitons, modeled by the Schrödinger–Hirota equation, numerically by the aid of the Adomian decomposition. The surface plots of the algorithm yielded an impressively small measure. The effects of soliton radiation are ignored. [ABSTRACT FROM AUTHOR]

This paper retrieves an optical 1–soliton solution to a model that is written as a concatenation of the Lakshmanan–Porsezian–Daniel model and Sasa–Satsuma equation. The method of undetermined coefficients obtains a full spectrum of 1–soliton solutions. The multiplier approach yields the conserved densities, which subsequently lead to the conserved quantities from the bright 1–soliton solution. [ABSTRACT FROM AUTHOR]

The current work addresses cubic–quartic solitons to compensate for the low count of the chromatic dispersion that is one of the major hindrances of soliton transmission through optical fibers. Thus, the present paper handles the cubic–quartic version of the perturbed Fokas–Lenells equation that governs soliton communications across trans-oceanic and trans-continental distances. The model is also considered with the power-law form of nonlinear refractive index that is a sequel to the previously reported result. This is a tremendous advancement to the previously known result that was only with the Kerr-law form of nonlinear refractive index. The present paper mainly contributes by generalizing the Kerr law of nonlinearity to the power law of nonlinearity. The prior results therefore fall back as a special case to the results of this paper. The semi-inverse variational principle yields a bright 1-soliton solution that is imperative for the telecommunication engineers to carry out experimental investigation before the rubber meets the road. Hamiltonian perturbation terms are included that come with maximum intensity. The soliton amplitude–width relation is retrievable from a polynomial equation with arbitrary degree. The parameter constraints are also identified for the soliton to exist. [ABSTRACT FROM AUTHOR]

This paper carries out numerical simulations of highly dispersive optical solitons with differential group delay having quadratic-cubic law of nonlinearity. The Laplace–Adomian decomposition scheme is implemented to visualize the soliton propagation dynamics. Both bright and dark solitons are addressed. The error measure for these numerical approximations is impressively low as presented. [ABSTRACT FROM AUTHOR]

This paper serves as a sequel to previously reported results on cubic‐quartic solitons with complex Ginzburg–Landau equation. This work is with various forms of power law nonlinearity that structures the self‐phase modulation. The enhanced Kudryashov's approach gives the soliton solution. The conservation laws are also identified for the models. [ABSTRACT FROM AUTHOR]

This paper numerically addresses bright optical solitons with cubic-quintic-septic (polynomial) law of nonlinear refractive index. The adopted scheme is with Adomian decomposition. The surface and contour plots are presented along with negligibly small error count. [ABSTRACT FROM AUTHOR]

This paper is a numerical simulation of highly dispersive optical solitons in birefringent fibers with polynomial nonlinear form, which is achieved for the first time. The algorithmic approach is applied with the usage of the Laplace–Adomian decomposition scheme. Dark and bright soliton simulations are presented. The error measure has a very low count, and thus, the simulations are almost an exact replica of such solitons that analytically arise from the governing system. The suggested iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. [ABSTRACT FROM AUTHOR]

The current work recovers a perturbed bright 1-soliton solution to the governing model that maintains generalized quadratic–cubic nonlinearity. The perturbation terms appear with full intensity. The semi-inverse variational principle secures this soliton when all of the known approaches fail, in this regard. [ABSTRACT FROM AUTHOR]

We study numerically highly dispersive optical solitons in birefringent fibres, which arise from a non-local form of nonlinear refractive index. A Laplace– Adomian decomposition scheme is used as integration algorithm. Both bright and dark solitons are addressed. The error plots obtained by us indicate an extremely appealing error measure. [ABSTRACT FROM AUTHOR]

This work analytically recovers the highly dispersive bright 1–soliton solution using for the perturbed complex Ginzburg–Landau equation, which is studied with three forms of nonlinear refractive index structures. They are Kerr law, parabolic law, and polynomial law. The perturbation terms appear with maximum allowable intensity, also known as full nonlinearity. The semi-inverse variational principle makes this retrieval possible. The amplitude–width relation is obtained by solving a cubic polynomial equation using Cardano's approach. The parameter constraints for the existence of such solitons are also enumerated. [ABSTRACT FROM AUTHOR]

This work studies cubic–quartic optical solitons with Kudryashov's law of refractive index. The extended trial function approach reveals solutions to the model in terms of Jacobi's elliptic functions that yields bright and singular optical solitons with limiting values to the modulus of ellipticity. The conservation laws are also presented. [ABSTRACT FROM AUTHOR]

We reveal cubic--quartic optical solitons with quadratic--cubic nonlinearity for the first time. Both polarization-preserving and birefringent optical fibres are considered. The study is also extended to include the perturbation terms of Hamiltonian type. The integration algorithm adopted in the present work is the method of sine-Gordon equation. [ABSTRACT FROM AUTHOR]

For the first time in the field of nonlinear optics, we address cubic--quartic solitons appearing in the fibre Bragg gratings with dispersive reflectivity for four different cases of nonlinear refractive-index structures. A complete spectrum of single solitons, together with some straddled solitons, emerges from the integration scheme adopted by us, which is the approach of sine--Gordon equation. [ABSTRACT FROM AUTHOR]

This work recovers cubic–quartic soliton solutions to the Lakshmanan–Porsezian–Daniel model by the method of undetermined coefficients. Both polarization-preserving fibers and birefringent fibers are studied. The conservation laws for polarization-preserving fibers are also retrieved and enumerated. The existence criteria for the displayed solitons are also presented. [ABSTRACT FROM AUTHOR]

We retrieve analytically a bright 1-soliton solution to a perturbed cubic-quartic Lakshmanan-Porsezian-Daniel model, using a semi-inverse variational principle. The perturbation terms are considered arising from the condition of maximum allowable intensity. The restrictions imposed by integrability considerations on the model parameters are enlisted. It is important that the other analytical approaches available fail to recover the analytical bright-soliton solution to the model with the maximum allowable intensity. [ABSTRACT FROM AUTHOR]

This paper obtains the bright, singular and combo solitons solutions in birefringent fibers, with four-wave mixing, that maintains quadratic-cubic law of refractive of refractive index, by implementing traveling wave hypothesis. Adomian decomposition method is subsequently applied to the obtained results on bright solitons to display its numerical simulation with an impressive error measure. [ABSTRACT FROM AUTHOR]

This paper studies bright highly dispersive optical solitons that are with nonlocal type of nonlinearity. The numerical scheme, adopted in the paper, is Laplace-Adomian method. The analytical results, reported earlier, and the numerical results from the current work, agree with an impressively small error measure. [ABSTRACT FROM AUTHOR]

Cubic-quartic soliton transmission having power law of nonlinearity refractive index. • Optical soliton solutions for the perturbed nonlinear Schrodinger's equation are revealed. • Quadratic-cubic nonlinearity is considered. • Bright optical solitons are retrieved by the help of the IADM. • The numerical results together with high level accuracy plots are exhibited. • The method proposed herein works with high degree of accuracy. This paper numerically retrieves cubic-quartic solitons having power law of nonlinearity refractive index. An improvement of the Adomian decomposition scheme is the adopted algorithm of this work. The results are displayed along with the established error analysis. [ABSTRACT FROM AUTHOR]

This paper recovers quiescent optical solitons for the complex Ginzburg–Landau equation, studied with nonlinear chromatic dispersion and three of Kudryashov’s self–phase modulation structures. The enhanced Kudryashov's procedure has made retrieving a full spectrum of solitons possible. [ABSTRACT FROM AUTHOR]

This study aims to investigate cubic-quartic optical solitons with Kudryashov’s law of self-phase modulation. Thus, the combination of third-order dispersion (3OD) and fourth-order dispersion (4OD) is assumed in the model to ensure the smooth existence of solitons. The study is implemented with the aid of two effective integration schemes known as the improved projective Riccati equations method and the soliton ansatz technique. The soliton solutions are derived based on two physical cases targeting the relation between 3OD and 4OD. In case 3OD is equivalent to fourfold frequency times 4OD, only dark and singular soliton profiles are extracted. However, if the former relation is not achieved, various structures of soliton pulses are generated, including kink-dark, singular, W-shaped, bright, dark, kink, and anti-kink solitons. The physical interpretations of retrieved optical solitons are represented by illustrating the wave behaviors with suitable values of model parameters. The results show that the combination of 3OD and 4OD has a significant effect on the dynamics of soliton propagation. [ABSTRACT FROM AUTHOR]

Soliton perturbation theory is used in this paper to uncover the adiabatic conservation laws. The effect of soliton cooling arises from a fixed point in the corresponding dynamical system. • This paper addresses the behavior of quasi-monochromatic solitons exhibiting a triple-power law of nonlinearity. • The power and linear momentum conserved quantities are derived by utilizing soliton perturbation theory. • The presence of a fixed point in the derived dynamical system leads to the cooling effect observed in optical solitons. [ABSTRACT FROM AUTHOR]

This work carries out the bifurcation analysis of the concatenation model that arises from nonlinear fiber optics. The fixed points of the dynamical system are recovered and classified. The Hamiltonian of the system is presented. The phase portraits of the system are also addressed. Subsequently, integrating along the periodic orbit, the soliton solutions for the model are retrieved. • A concatenation model that arises from nonlinear fiber optics is addressed in this paper. • The bifurcation analysis and fixed point analysis of the concatenation model are employed for the first time. • Soliton solutions are recovered by integration of the dynamical system along the periodic orbits. [ABSTRACT FROM AUTHOR]

Highly dispersive optical solitons are obtained for nonlinear Schrödinger's equation that is studied in absence of self-phase modulation. The effect of nonlinearity comes from perturbation terms. Jacobi's elliptic function expansion reveals bright and dark soliton solutions to the model. [ABSTRACT FROM AUTHOR]

This paper employs F -expansion scheme to retrieve highly dispersive optical solitons when self-phase modulation is negligibly small and hence discarded. A complete spectrum of solitons are nevertheless recovered for the model. [ABSTRACT FROM AUTHOR]

This paper studies optical solitons in birefringent fibers with anti-cubic nonlinearity. The exp-function scheme retrieves singular and combo solitons. The existence criteria for these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper studies highly dispersive optical solitons when self-phase modulation term is completely absent. The delicate balance for existence and sustaining of solitons is provided by self-steepening effect and nonlinear dispersions. The exp-function approach yields singular and bright-singular combo solitons. [ABSTRACT FROM AUTHOR]

This paper obtains highly dispersive singular optical solitons in cubic–quintic–septic nonlinear medium. The exp-function expansion is the applied integration algorithm. The solitons appear with their corresponding existence criteria. [ABSTRACT FROM AUTHOR]

This paper recovers singular and bright-singular highly dispersive optical solitons, having non-local form of nonlinearity, by the application of exp-function integration scheme. The existence criteria for these solitons are also listed in the work. [ABSTRACT FROM AUTHOR]

This paper studies highly dispersive optical solitons by the application of exponential function. The model is with quadratic–cubic nonlinear fibers. The algorithm reveals singular and bright–singular combo soliton solutions. The integrability criteria are also listed in this work. [ABSTRACT FROM AUTHOR]

This paper obtains bright and singular optical solitons that are studied with anti-cubic nonlinearity in birefringent fibers. The extended trial function scheme gave way to these results. The existence criteria of such solitons are also indicated. [ABSTRACT FROM AUTHOR]

This paper reveals bright, dark and singular solitons in fiber Bragg gratings with dispersive reflectivity having parabolic form of nonlinearity. The method of undetermined coefficients yielded such soliton solutions. The existence criteria of such solitons are also enumerated that are listed as constraint conditions. [ABSTRACT FROM AUTHOR]

In this work, symmetry reduction for nonlinear Schrödinger's equation with anti-cubic nonlinearity is determined by using the invariance of equations under Lie group of transformations. Using the similarity transformations the equation is reduced into system of ordinary differential equations. Corresponding to reduced ordinary differential equations, some exact solutions are obtained. These yields bright solitons, dark solitons, singular solitons and other explicit solutions. It is also pointed out that some of the results reported earlier are particular forms of current solutions. [ABSTRACT FROM AUTHOR]

This paper secures bright optical solitons in presence of third and fourth order dispersion terms while group velocity dispersion term is absent. The perturbation terms that are included appear with full nonlinearity. The semi-inverse variational principle is implemented to secure such solutions. [ABSTRACT FROM AUTHOR]

This paper secures bright-singular combo highly dispersive optical solitons by the application of exponential-function method. Several other solutions also emerged from the scheme although they are not applicable in nonlinear optics. The solitons appear with their respective integrability criteria that are also presented in this work. [ABSTRACT FROM AUTHOR]

This paper studies optical solitons in fiber Bragg gratings, that appear with quadratic–cubic nonlinearity, in presence of dispersive reflectivity. The extended trial function scheme revealed bright and singular optical soliton solutions to the model. The phase-matching condition was adopted to this model. [ABSTRACT FROM AUTHOR]