The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

Abstract

An essential aspect of mathematical physics is the PHI-four equation, which is a specific version of the Klein–Gordon equation that predicts particle physics phenomena. The present paper addresses numerical approaches to generalized PHI-four equation based on Laplace Adomian Decomposition Technique (LADT) which is governed by coupling of Laplace transform and Adomian decomposition method to determine the kink-antikink single waves in dispersion systems arises in mathematical physics. The nonlinear terms in the PHI-four equation are handled using the accelerated polynomial i.e., Adomian polynomial. The approach is extremely interesting computationally and is straightforward to execute. The accuracy and robustness of the current scheme are demonstrated by four test problems. To demonstrate the efficacy of our suggested approach, the current result is contrasted with both the analytical solution and existing solutions in literature. Stability and convergence analysis are well developed to justify the applicability of the current approach.