Lie group analysis of modified Camassa-Holm and 3D Kadomtsev-Petviashvili-like equations

Abstract

In this work, we investigate two nonlinear partial differential equations that possess real-world applications, namely the generalized simplified Camassa-Holm and (3+1)-dimensional Kadomtsev-Petviashvili like equation. Invoking Lie group analysis, we reduce the differential order of the equations or systematically find optimal variable changes, with an aim of finding analytica solutions. In addition, techniques inclusive of direct integration, simplest equation method and Kudryashov's approach are implored in this research. Furthermore, we construct conserved vectors for the underlying equations where diverse dimensional providings of selected solutions are presented. Method for securing conserved vectors of differential equations which comprise Noether's approach, multiplier technique as well a Ibragimov's conservation theorem are implored.