New Explicit Solutions of the Zoomeron Equation Using Optimum Indexing Approach

Abstract

This paper presents the nonlinear physical model called the (2+1)-dimensional Zoomeron Equation that is one of the equations describing incognito evolution. We apply the Power Index Method (PIM) to find analytic solutions of the equation by using function transformation. The PIM is a straight arithmetical technique in which the indexes of independent variables are adjusted in our chosen similarity transformation so that partial differential equations may be efficiently reduced to ordinary differential equations. Several exact solutions of the nonlinear Zoomeron equation are constructed, which are graphically represented for certain values of constant parameters. The suggested approach has been successfully used to identify new precise solutions for the nonlinear Partial Differential Equation (PDE).