Lie symmetry analysis, exact analytical solutions and dynamics of solitons for (2 + 1)-dimensional NNV equations

Abstract

In this present article, we devote our study on (2 + 1)-dimensional Nizhnik-Novikov-Vesselov (NNV) equations. To achieve our goal, we utilize various mathematical methods, namely Lie symmetry method, the Exp-function method and N-soliton solutions methods, and attain exact analytical solutions in numerous forms of the NNV system. Firstly, we generate infinitesimal generators, geometric vector fields, commutation relations of Lie algebra, and one-dimensional optimal system of the NNV equations. By using the Lie symmetry reduction method, the (2 + 1)-dimensional NNV system of equations is reduced to a (1+1)-dimensional partial differential equations (PDEs). Thereafter, we apply the Exp-function method to the reduced NNV equations with the aid of symbolic computation via Mathematica. The exact analytical solutions are obtained in the forms of different wave structures of solitons, doubly solitons, Weierstrass solution, lump-type solitons, bright solitons and dark solitons, parabolic solitary wave, trigonometric and hyperbolic solitons. All the obtained exact analytical solutions are new in the formulation and never reported in the literature as per the author’s knowledge. The dynamics of different wave structures of solitons are illustrated graphically using two, three-dimensional graphics and contour plots. The graphs are more effective and advantageous to physicists and mathematicians for following the complex physical phenomena.