Cnoidal and snoidal waves and conservation laws for physical space-time (3 + 1)-dimensional modified KdV models

Abstract

The aim of this paper is to study three space-time (3 + 1)-dimensional modified Korteweg-de Vries equations. Nonlinear space-time (3 + 1)-dimensional partial differential equations model many realistic problems in the fields of engineering, wave propagation, fluids, etc. Firstly we construct exact closed-form solutions for the three (3 + 1)-dimensional modified Korteweg-de Vries equations using Lie symmetry method together with the extended Jacobi elliptic expansion method. The solutions obtained are soliton, cnoidal and snoidal waves. Secondly we determine conservation laws for the underlying equations using the multiplier method. Keywords: (3 + 1)-dimensional modified KdV equation, Lie point symmetries, Exact closed-form solutions, Conservation laws