The Classification of the Exact Single Travelling Wave Solutions to the Constant Coefficient KP-mKP Equation Employing Complete Discrimination System for Polynomial Method

The purpose of this article is to explore different types solutions for the Kadomtsev-Petviashvili-modified Kadomtsev-Petviashvili (KP-mKP) equation which termed as KP-Gardner equation, extensively used model strong nonlinear internal waves in ( 1 + 2 )-dimensions on stratified ocean shelf. This evolution also describe weakly shallow-water wave and dispersive interracial traveling a mildly rotating channel with slowly varying topography. Introducing Liu’s approach regarding complete discrimination system polynomial trial technique, set new KP-mKP containing Jacobi elliptic function have been derived. It found that these analytical numerically exhibit structures such solitary waves, shock periodic profiles. reliability effectiveness are confirmed from numerical graphs solutions. Finally, existence validity various topological phase portrait dynamical system. Based investigation, it method not only suited obtaining classification but qualitative analysis, means can be extended other fields application.