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Lie symmetry analysis, optimal system, and generalized group invariant solutions of the (2 + 1)‐dimensional Date–Jimbo–Kashiwara–Miwa equation
Author(s) -
Chauhan Astha,
Sharma Kajal,
Arora Rajan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6547
Subject(s) - mathematics , homogeneous space , invariant (physics) , infinitesimal , lie group , lie theory , commutator , mathematical analysis , soliton , nonlinear system , symmetry group , mathematical physics , adjoint representation , pure mathematics , adjoint representation of a lie algebra , quantum mechanics , physics , geometry , lie conformal algebra
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.