Lie symmetry reductions and generalized exact solutions of Date–Jimbo–Kashiwara–Miwa equation

Abstract

The propagation of nonlinear waves with nonuniform velocities is described by nonlinear evolution equations and their solutions involving arbitrary functions. When a nonlinear evolution equation is integrated, it reveals the several existing features of natural phenomena with continuous and fluctuating background. The Date–Jimbo–Kashiwara–Miwa equation is long water wave equation, which describes the propagation of nonlinear and weakly dispersive waves in inhomogeneous media. This work aims to extend the previous results and derive symmetry reductions of Date–Jimbo–Kashiwara–Miwa equation via Lie symmetry method. The infinitesimals involving four arbitrary functions are constructed by preserving invariance property of Lie groups under one parameter transformations. Then, the first symmetry reduction of test equation is determined using symmetry variables. The commutative and adjoint relations of four dimensional subalgebra are presented for reduced equation. Thereafter, the repeated utilization of Lie symmetry method results into the ordinary differential equations. These determining ODEs are solved under numeric constraints and provide exact solutions. The derived solutions retain all the four arbitrary functions appeared in infinitesimals and several arbitrary constants. Due to existing arbitrary functions, these solutions are generalized than previous established results. The deductions of previous results (Wang et al., 2014; Ali et al., 2021; Chauhan et al., 2020; Kumar and Kumar, 2020; Tanwar and Kumar, 2021; Kumar and Manju, 2022) show the novelty and significance of these solutions. Moreover, the derived results are expanded systematically with numerical simulation to analyze their physical significance and thus doubly soliton, multisoliton, line soliton, bell shape, parabolic nature are discussed.