Generalized Functional Equations of Polylogarithmic Groups

Abstract

In this article, the Laplace decomposition method is implemented to solve nonlinear partial differential equations. Third-order KdV and mKdV equations with initial conditions have been considered to check the validity of the proposed method. Results obtained by this method are compared with the exact solutions in literature numerically as well as graphically and are found to be in good agreement with each other. The proposed method finds the solutions without any discretization, perturbation, linearization, or restrictive assumptions. Obtained results show that the LDM is highly accurate and easy to apply for NLPDEs in various fields.