Symmetry analysis and soliton solution of (2+1)- dimensional Zoomeron equation

TL;DR

This paper employs Lie group analysis and similarity transformations to derive traveling wave and soliton solutions of the (2+1)-dimensional Zoomeron equation, demonstrating the effectiveness of symmetry methods in solving nonlinear PDEs in mathematical physics.

Contribution

It applies the novel Lie group method and similarity transformation technique to obtain exact solutions of the (2+1)-dimensional Zoomeron equation, reducing it to simpler equations.

Findings

Traveling wave solutions expressed in exponential functions.

Reduction of (2+1)-D PDEs to (1+1)-D PDEs and ODEs.

Exact solutions demonstrating the applicability of symmetry methods.

Abstract

Traveling wave solutions of (2 + 1)-dimensional Zoomeron equation(ZE) are developed in terms of exponential functions involving free parameters. It is shown that the novel Lie group of transformations method is a competent and prominent tool in solving nonlinear partial differential equations(PDEs) in mathematical physics. The similarity transformation method(STM) is applied first on (2 + 1)-dimensional ZE to find the infinitesimal generators. Discussing the different cases on these infinitesimal generators, STM reduce (2 + 1)-dimensional ZE into (1 + 1)-dimensional PDEs, later it reduces these PDEs into various ordinary differential equations(ODEs) and help to find exact solutions of (2 + 1)-dimensional ZE.