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Abstract: The generalized Burgers equation with generalized evolution is studied in this paper. The soliton ansatz is used to carry out the integration of this generalized Burgers equation. This study is then extended to 1+2 dimensions, even with full nonlinearity. [Copyright &y& Elsevier]

Abstract: This paper obtains the 1-soliton solution of the nonlinear dispersive Drinfel’d–Sokolov equation with power law nonlinearity. In the first case the soliton solution is without the generalized evolution. The solitary wave ansatz method is used to carry out the integration. Subsequently, the He’s semi-inverse variational principle is used to integrate the equation with power law nonlinearity. Parametric conditions for the existence of envelope solitons are given. [Copyright &y& Elsevier]

Abstract: This paper studies the Zakharov equation with power law nonlinearity. An exact 1-soliton solution is obtained by the ansatz method. The parameter regimes are identified in the process. The numerical simulation is also given to complete the study. [Copyright &y& Elsevier]

Abstract: This paper obtains the 1-soliton solution of a nonlinear wave equation that arises in the study of semiconductors. The conserved quantities are also calculated from this equation. Furthermore, additional non-trivial conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler–Lagrange operator annihilates the total divergence. [ABSTRACT FROM AUTHOR]

Abstract: This paper obtains the 1-soliton solution of the Klein–Gordon–Zakharov equation with power law nonlinearity. The solutions are obtained both in (1+1) and (1+2) dimensions. The solitary wave Ansatz method is applied to obtain the solution. The numerical simulations are included that supports the analysis. [ABSTRACT FROM AUTHOR]

Abstract: This paper obtains the 1-soliton solution of the Klein–Gordon–Schrödinger’s equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. Both 1+1, 1+2 and 1+N dimensional cases are considered. [ABSTRACT FROM AUTHOR]

Abstract: This paper obtains the exact 1-soliton solution to the nonlinear Schrödinger’s equation with log law nonlinearity in presence of time-dependent perturbations. The dispersion and nonlinearity are also taken to be time-dependent. The perturbation terms that are considered are linear attenuation and inter-modal dispersion. The constraint condition between the time-dependent coefficients also fall out as a necessary condition for the solitons to exist. [Copyright &y& Elsevier]

Abstract: In this paper, the topological 1-soliton solution to the generalized Korteweg–de Vries equation with generalized evolution will be obtained. The solitary wave ansatz methods will be applied to obtain the solutions. In the process, the constraints relations between the soliton parameters will also be determined. [ABSTRACT FROM AUTHOR]

Abstract: This paper obtains the exact 1-soliton solution of the perturbed Korteweg–de Vries equation with power law nonlinearity. The topological soliton solutions are obtained. The solitary wave ansatz is used to carry out this integration. The domain restrictions are identified in the process and the parameter constraints are also obtained. It has been proved that topological solitons exist only when the KdV equation with power law nonlinearity reduces to simply KdV equation. [ABSTRACT FROM AUTHOR]

Abstract: This paper obtains the 1-soliton solution of the complex KdV equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. The soliton perturbation theory for this equation is developed and the soliton cooling is observed for bright solitons. Finally, the dark soliton solution is also obtained for this equation. [ABSTRACT FROM AUTHOR]

Abstract: This paper obtains the 1-soliton solution of the Jaulent–Miodek equation with power law nonlinearity. The solitary wave ansatz is used to obtain the soliton solution to this equation. Subsequently, the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler–Lagrange operator annihilates the total divergence. [ABSTRACT FROM AUTHOR]

Abstract: This paper obtains the 1-soliton solution of the generalized Dullin–Gottwald–Holm equation by the aid of solitary wave ansatz. Subsequently, the conserved quantities are obtained by utilising the interplay between the multipliers and underlying Lie point symmetry generators of the equation. [ABSTRACT FROM AUTHOR]

Abstract: This paper carries out the integration of the coupled KdV equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. The domain restrictions of the coefficients of nonlinear and dispersion terms fall out. The results are then supplemented by numerical simulations. [Copyright &y& Elsevier]

Abstract: This paper studies the soliton perturbation that are described by three nonlinear wave equations. The adiabatic dynamics of the soliton parameters and the soliton velocity is obtained, in the presence of perturbation terms. The fixed point is also determined in a couple of cases. [Copyright &y& Elsevier]

Abstract: This paper obtains the 1-soliton solution of three variants of the generalized KdV equation with generalized evolution. The solitary wave ansatz is used to carry out the integration of such equation. The parameter domain is also identified in the process. A couple of conserved quantities are also calculated for each of these variants. The numerical simulations are also carried out. [Copyright &y& Elsevier]

Abstract: This paper obtains the 1-soliton solution to Zakharov equation with power law and dual-power law nonlinearities. The He’s variational principle is used to carry out the integration of this equation. [Copyright &y& Elsevier]

Abstract: This paper obtains the 1-soliton solution of five various forms of the generalized nonlinear Klein–Gordon equations. The solitary wave ansatz is used to obtain the soliton solutions of each of these cases. Both topological as well as non-topological soliton solutions are obtained depending on the type of nonlinearity in question. The conserved quantities are also calculated for each of these five forms of generalized nonlinear Klein–Gordon equations. Each of these forms reduce to the previously known results, as special cases. [Copyright &y& Elsevier]

Abstract: This paper obtains the closed form optical 1-soliton solution of the nonlinear Schrödinger’s equation, with parabolic law nonlinearity, in presence of the fourth order dispersion. The restrictions on the parameters of the soliton are also calculated in course of the derivation of the soliton solution. [Copyright &y& Elsevier]

Abstract: This paper studies the adiabatic dynamics of soliton velocity due to the quadratic Klein–Gordon equations, in presence of perturbation terms. The soliton perturbation theory is exploited for 1-soliton solution of this equation. [Copyright &y& Elsevier]

Abstract: The dispersion-managed optical solitons is studied in this paper in presence of various perturbation terms. The Gaussian solitons are considered and the dynamics of such pulses are obtained in presence of such perturbation terms. The integrals of motion are evaluated. The soliton perturbation theory is exploited to formulate the parameter dynamics of the Gaussian solitons. [Copyright &y& Elsevier]

Abstract: The intra-channel collision of optical solitons, with dual-power law nonlinearity, is studied in this paper by the aid of quasi-particle theory. The perturbation terms that are considered in this paper are of Hamiltonian type. The suppression of soliton–soliton interaction, in presence of these perturbation terms, is acheived. The numerical simulations support the quasi-particle theory. [Copyright &y& Elsevier]

The soliton perturbation theory is used to obtain the adiabatic parameter dynamics of solitons in magneto-optic waveguides. This is governed by the generalized vector nonlinear Schrodinger''s equation. [Copyright &y& Elsevier]

This paper is a theoretical study of solitons governed by the nonlinear Schrödinger''s equation (NLSE) with non-Kerr law nonlinearity. The soliton perturbation theory is used to obtain the parameter dynamics of solitons that are governed by this equation. This study is extended to the case of the vector NLSE and its further generalization. In addition, we have studied the adiabatic parameter dynamics of solitons in presence of perturbation terms. [Copyright &y& Elsevier]

The soliton perturbation theory is used to obtain the adiabatic parameter dynamics of the perturbed solitons that are governed by the generalized nonlinear Schrodinger’s equation. The perturbation terms considered in this paper are of dispersive, dissipative as well of nonlocal type. [Copyright &y& Elsevier]

The soliton perturbation theory is used to obtain the adiabatic parameter dynamics of the perturbed vector solitons that are governed by the generalized non-linear Schrodinger’s equation. The perturbation terms considered in this paper are of dispersive, dissipative as well of non-local type. [Copyright &y& Elsevier]

Abstract: This paper studies the Kadomtsev–Petviasvili equation with power law nonlinearity. Topological 1-soliton solution is obtained and the parameter domain is identified for these solitons to exist. The solitary wave ansatz is used to obtain this solution. [ABSTRACT FROM AUTHOR]

Abstract: This paper obtains the 1-soliton solution of the Kadomtsev–Petviasvili equation with power law nonlinearity using the solitary wave ansatz. An exact soliton solution is obtained and a couple of conserved quantities are also computed. [Copyright &y& Elsevier]

We study the soliton like behavior and conservation laws of a model that describes weakly nonlinear oceanic internal waves when two distinct linear long wave modes have nearly coincident phase speeds. The equations governing the model is the systems equivalent of the Ostrovsky equation. [ABSTRACT FROM AUTHOR]

Abstract: This paper applies the variational iteration method (VIM) and semi-inverse variational principle to obtain solutions of linear and nonlinear partial differential equations. The nonlinear model is considered from gas dynamics, fluid dynamics and Burgers equation. The linear model is the heat transfer (diffusion) equation. Results show that variational iteration method is a powerful mathematical tool for solving linear and nonlinear partial differential equations, and therefore, can be widely applied to engineering problems. [Copyright &y& Elsevier]

Abstract: This paper studies the mathematical structure of the kink soliton solution to the generalized dispersive SGE. All derivatives are found and the trigonometric functions of the kink are found for a generalized height. [Copyright &y& Elsevier]

Abstract: In this paper, the complex Korteweg–de Vries equation with power law nonlinearity is studied in presence of perturbation terms. The exact 1-soliton solution is obtained. It will be seen that the time-dependent coefficients must be simply Riemann integrable for the solitons to exist. The solitary wave ansatz is used to carry out the integration. [ABSTRACT FROM AUTHOR]

Abstract: This paper reflects the implementation of a reliable technique which is called modified simple equation method (MSEM) for solving evolution equations. The proposed algorithm has been successfully tested on two very important evolution equations namely Fitzhugh–Nagumo equation and Sharma–Tasso–Olver equation. Numerical results are very encouraging. [ABSTRACT FROM AUTHOR]

Abstract: This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV–Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method. [Copyright &y& Elsevier]

Abstract: In this paper, we study the Korteweg-de Vries (KdV) equation having time dependent coefficients from the Lie symmetry point of view. We obtain Lie point symmetries admitted by the equation for various forms for the time-dependent coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary coefficients. Subsequently, the 1-soliton solution is obtained by the aid of solitary wave ansatz method. It is observed that the soliton solution will exist provided that these time-dependent coefficients are all Riemann integrable. [Copyright &y& Elsevier]

Abstract: This paper carries out the integration of a few nonlinear wave equations to obtain topological as well as non-topological soliton solutions. The mathematical techniques used to obtain the soliton solutions are He’s variational iteration method, the tanh method and the ansatz method. The nonlinear wave equations that are studied are coupled mKdV equations, Drinfeld–Sokolov equation and its generalized version. Finally, some numerical simulations are given to support the analytical solutions. [Copyright &y& Elsevier]

Abstract: This paper obtains the 1-soliton solution of three variants of the generalized KP equation with generalized evolution. The solitary wave ansatz is used to carry out the integration of such equations. The parameter domain is also identified in the process. The numerical simulations are also obtained in this paper. [Copyright &y& Elsevier]

Abstract: This paper obtains the solitary wave as well as the shock wave solutions to the second order wave equation of Korteweg–de Vries type that was first proposed in 2002. The ansatz method is used to retrieve these solutions. The domain restrictions as well as the parameter regimes are all identified in the process of obtaining the solution. [Copyright &y& Elsevier]

Abstract: An analytical and numerical investigation of the propagation of optical beams in Kerr term-like saturable photorefractive media is performed. The major problem studied is the instability of beam propagation in nonlinear self-focusing optical media by the Runge–Kutta finite-difference numerical technique. The resulting soliton-like structures propagate and develop modulational instabilities which lead to the breakup of simple beam arrangements into more complex ones. The direct numerical simulation of the nonlinear Schrödinger’s equation with square-root law nonlinearity is performed. Gaussian, super-Gaussian, and sech pulses are obtained numerically. Finally the ordinary differential equation that is obtained by the traveling wave ansatz is also studied numerically, with appropriate initial condition, leading to a traveling wave-like solution. [Copyright &y& Elsevier]

• An extended NLSE with time-modulated coefficients is studied. • The nonautonomous bright soliton solutions are reported. • Propagation properties of those solitons are discussed. We investigate the existence and propagation properties of envelope solitons of an extended nonlinear Schr ödinger equation with the time-modulated dispersion, quadratic-cubic nonlinearities and linear gain or loss, which govern the nonlinear wave propagation in a nonautonomous quasi-1D Bose-Einstein condensate system with contact repulsion and dipole-dipole attraction. A novel class of nonautonomous bright soliton solutions on continuous-wave background is identified for the first time. It is shown that these localized structures possess interesting features that differ from the usual bright solitons. A rich variety of evolution behaviors, which include snakelike and periodic oscillating bright soliton dynamics, is revealed. The constraints of the system parameters to form these nonlinear localized structures are also suggested. [ABSTRACT FROM AUTHOR]

• A generalized (3+1)-dimensional Kadomtsev–Petviashvili equation is studied. • Hirota bilinear method is applied. • Lump solutions are reported. In this paper, a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation, which can be reduced to the classical equation, is investigated based on the Hirota bilinear method. The lump and lump strip solutions for this equation are obtained with the help of symbolic computation. Those solutions are derived from polynomial solutions, and can be simply classified into some classes. Analysis for the obtained solutions are presented, and their dynamic properties are discussed. Results are helpful for the study of soliton interactions in nonlinear mathematical physics. [ABSTRACT FROM AUTHOR]