Topological and non-topological solitons of the Klein–Gordon equations in 1+2 dimensions

This paper obtains the topological and non-topological 1-soliton solution of the Klein–Gordon equation in 1+2 dimensions. There are five various forms of this equation that will be studied. The solitary wave ansatz will be used to carry out the integration.     

Topological exact soliton solution of the power law KdV equation

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.     

Exact solutions of KdV equation with time-dependent coefficients

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.     

Soliton solutions of a few nonlinear wave equations

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.     

Optical soliton perturbation for Gerdjikov–Ivanov equation via two analytical techniques

This paper employs two integration procedures to obtain soliton solutions to the perturbed Gerdjikov–Ivanov equation. They are G′/G²–expansion method and the sine–cosine method. Bright, dark and singular solitons are revealed along with a few of the combo–soliton solutions. The existence criteria of these solitons are also given.     

1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation

This Letter carries out the integration of the generalized Radhakrishnan, Kundu, Lakshmanan equation to obtain the 1-soliton solution. The solitary wave ansatz is used to carry out the integration, to obtain an exact solution of this equation.     

1-Soliton Solution of the Nonlinear Schrödinger’s Equation with Kerr Law Nonlinearity Using Lie Symmetry Analysis

This paper obtains the 1-soliton solution of the nonlinear Schrödinger’s equation in a Kerr law media. The technique that is used to carry out the integration of this equation is the Lie symmetry analysis.     

Solitons in Plasmas: A Lie Symmetry Approach

This paper talks about the stationary solitons for Langmuir waves in plasmas that are described by the Nonlinear Schrödinger’s equation with power law nonlinearity. The integration is carried out by the usage of Lie symmetry in presence of perturbation terms.     

Doubly Periodic Solution for Nonlinear Schrödinger’s Equation With Higher Order Polynomial Law Nonlinearity

This paper obtains the travelling wave solutions of the nonlinear Schrödinger’s equation with higher order polynomial law nonlinearity. The doubly periodic wave solution of this equation is obtained. The numerical simulation is also included.     

Optical soliton perturbation in a non-Kerr law media

This paper studies the optical soliton perturbation by the aid of soliton perturbation theory. The various perturbation terms, that arise in the study of optical solitons, are exhaustively studied in this paper. The adiabatic parameter dynamics of optical solitons are obtained in presence of these perturbation terms. The types of nonlinearities that are considered are Kerr law, power law, parabolic law as well as the dual-power law.