Travelling Wave Solutions and Conservation Laws of the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation (Journal of Nonlinear Modeling and Analysis, 2024)
The travelling wave solutions and conservation laws of the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) equation are considered in thispaper. Under the travelling wave frame, the BKK equation is transformed to asystem of ordinary differential equations (ODEs) with two dependent variables.Therefore, it happens that one dependent variable $u$ can be decoupled intoa second order ODE that corresponds to a Hamiltonian planar dynamicalsystem 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 theBBK equation are derived by employing the multiplier approach.