Gangwei Wang

Invariant analysis and explicit solutions of the time fractional nonlinear perturbed Burgers equation

The Lie group analysis method is performed for the nonlinear perturbed Burgers equation and the time fractional nonlinear perturbed Burgers equation. All of the point symmetries of the equations are constructed. In view of the point symmetries, the vector fields of the equations are constructed. Subsequently, the symmetry reductions are investigated. In particular, some novel exact and explicit solutions are obtained.

Optical soliton of time fractional Schrödinger equations with He’s semi-inverse method

This paper addresses time fractional Schr?dinger equations?using He?s semi-inverse method. The (3?+?1)-dimensional time fractional Schr?dinger equation?and the time fractional unstable nonlinear Schr?dinger equation?are considered. 1-soliton solution is constructed for these two time fractional Schr?dinger equations. In particular, the parameters? constraint conditions are also derived for the existance of solitons. The method is straightforward and concise for solving differential equations.

Group Analysis and New Explicit Solutions of Simplified Modified Kawahara Equation with Variable Coefficients

The simplified modified Kawahara equation with variable coefficients is studied by using Lie symmetry method. Then we obtain the corresponding Lie algebra, optimal system, and the similarity reductions. At last, we also give some new explicit solutions for some special forms of the equations.

Optical Solitons for the Perturbed Nonlinear Schrödinger Equation with Kerr Law and Non-Kerr Law Nonlinearity

Abstract This paper analyses the dynamics of soliton propagation through optical fibres for the perturbed nonlinear Schrödinger equation with Kerr law and non-Kerr law nonlinearity. Several integration schemes are used to construct solitons to the model. The two forms of nonlinearity that are studied in detail are power law and dual power law, while Kerr law and parabolic law emerge as special cases to these two laws.