New Exact Solutions for the ( 2 + 1 ) -Dimensional Broer-Kaup-Kupershmidt Equations

Abstract

We investigate the $(2+1)$-dimensional Broer-Kaup-Kupershmidt equations. Some explicit expressions of solutions for the equations are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain kink-shaped solutions, blow-up solutions, periodic blow-up solutions, and solitary wave solutions. Some previous results are extended.