Symmetry analysis and some new exact solutions of some nonlinear KdV-like equations

Abstract

In this paper, we obtained some new exact solutions of some nonlinear KdV-like equations using Lie point symmetry and [Formula: see text]-symmetry methods. The obtained solutions are in the form of doubly periodic, bright and dark soliton solutions.

Symmetry Analysis and Some New Exact Solutions of the (2+1)-dimensional Burgers Equations

“…The solutions of nonlinear differential equations are an essential tool for many physical and engineering applications. There are many methods to solve nonlinear partial differential equations (PDEs) such as the Weierstrass function method [1], Jacobi elliptic function method [2,3], Hirota bilinear method [4], the inverse scattering method [5], the tanh method [6], the extended mapping transformation method [7], the truncated expansion method [8], the simplest equation method [9], the bifurcation method [10] and Lie symmetry method [11][12][13][14]. The latter is considered as the most powerful method for getting exact solutions of PDEs.…”