Lie symmetries, exact solutions and conservation laws of the Date–Jimbo–Kashiwara–Miwa equation

Abstract

Solitary waves are usually outcome of nonlinear and dispersive effects. The Date–Jimbo–Kashiwara–Miwa equation is dispersive and highly nonlinear soliton equation. The Date–Jimbo– Kashiwara–Miwa equation is a well-known integrable generalization of the KP equation and represents evolution of propagating waves in nonlinear dispersive media. It has wave dispersion changing properties in nonlinear dynamics. In this work, we aim to carry out symmetry reductions and exact solutions of the Date–Jimbo–Kashiwara–Miwa equation using Lie point symmetries. The possible infinitesimal generators and infinite-dimensional algebra of symmetries are constructed by utilizing the invariance property of Lie groups. Then, similarity variables are used to reduce the test problem and lead to determining ordinary differential equations. These equations provide desired exact solutions under some parametric constraints. The derived solutions are generalized than previous established results and have never been reported yet. Moreover, the self-adjoint equation and conserved vectors with associated symmetries are established under the Lagrangian formulation. To demonstrate the significance of interaction phenomena, the solutions have been extended with numerical simulation. Consequently, stripe soliton, line soliton, multisoliton, soliton fission, parabolic profile and their elastic nature are discussed systematically to validate these solutions with physical phenomena.