TY - JOUR
T1 - Travelling Wave Solutions and Conservation Laws of the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation
AU - Zhang , Lijun
AU - Simbanefayi , Innocent
AU - Khalique , Chaudry Masood
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 421
EP - 430
PY - 2022
DA - 2022/06
SN - 3
DO - http://doi.org/10.12150/jnma.2021.421
UR - https://global-sci.org/intro/article_detail/jnma/20671.html
KW - The (2+1)-dimensional Broer-Kaup-Kupershmidt equation, Travelling wave solutions, Conservation laws, Multiplier method.
AB - <p style="text-align: justify;">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.</p>