Physics

Nonlinear system

Invariant (physics)

Pure mathematics

Mathematics

Mathematical physics

Infinitesimal

Commutator

Mathematical analysis

Lie theory

Adjoint representation of a Lie algebra

Lie group

Geometry

Adjoint representation

Quantum mechanics

Homogeneous space

Symmetry group

Lie conformal algebra

Soliton

Mathematical Methods in the Applied Sciences

In this work, Lie group theoretic method is used to carry out the similarity reduction and solitary wave solutions of (2 + 1)‐dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) equation. The equation describes the propagation of nonlinear dispersive waves in inhomogeneous media. Under the invariance property of Lie groups, the infinitesimal generators for the governing equation have been obtained. Thereafter, commutator table, adjoint table, invariant functions, and one‐dimensional optimal system of subalgebras are derived by using Lie point symmetries. The symmetry reductions and some group invariant solutions of the DJKM equation are obtained based on some subalgebras. The obtained solutions are new and more general than the rest while known results reported in the literature. In order to show the physical affirmation of the results, the obtained solutions are supplemented through numerical simulation. Thus, the solitary wave, doubly soliton, multi soliton, and dark soliton profiles of the solutions are traced to make this research physically meaningful.

Lie symmetry analysis, optimal system, and generalized group invariant solutions of the (2 + 1)‐dimensional Date–Jimbo–Kashiwara–Miwa equation