New Explicit Solutions of Zoomeron Equation Using Optimal Indexing Approach

Abstract

This paper presents a nonlinear physical model called the (2+1)-dimensional Zomeron equation, which is one of the equations that describes latent evolution. We apply the Power Index Method (PIM) to find analytical solutions of equations using function transformations with optimal indexing of one variable. After selecting index of the variable, then we adopt function transform of another variable that make sure all coefficient terms to change in new variable. PIM is a straightforward mathematical technique in which the indices of the independent variables are adjusted to our selected similarity transformations to effectively reduce the partial differential equation to an Ordinary Differential Equation (ODE). Several exact solutions of the nonlinear Zoumron equation have been built and are presented graphically for some values of the constant parameters. The proposed method has been effectively used to find new exact solutions of nonlinear PDE. Using these transforms, we can easily produce infinitesimal generators of the PDE.