Travelling Wave Solutions and Conservation Laws of the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation
Year: 2021
Author: Lijun Zhang, Innocent Simbanefayi, Chaudry Masood Khalique
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 3 : pp. 421–430
Abstract
The travelling wave solutions and conservation laws of the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) equation are considered in this paper. Under the travelling wave frame, the BKK equation is transformed to a system of ordinary differential equations (ODEs) with two dependent variables. Therefore, it happens that one dependent variable $u$ can be decoupled into a second order ODE that corresponds to a Hamiltonian planar dynamical system involving three arbitrary constants. By using the bifurcation analysis, we obtain the bounded travelling wave solutions $u,$ which include the kink, anti-kink and periodic wave solutions. Finally, the conservation laws of the BBK equation are derived by employing the multiplier approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2021.421
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 3 : pp. 421–430
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: The (2+1)-dimensional Broer-Kaup-Kupershmidt equation Travelling wave solutions Conservation laws Multiplier method.