Travelling Wave Solutions and Conservation Laws of the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation

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.