Uniformly constructing combinatorial solutions, combining a rational function with hyperbolic or trigonometric functions, for the (2+1) dimensional Broer–Kaup–Kupershmidt equation

Abstract

According to two dependent rational solutions to a generalized Riccati equation together with the equation itself, a rational-exponent solution to a nonlinear partial differential equation can be constructed. By selecting different parameter values in the rational-exponent solution, many families of combinatorial solutions combined with a rational function such as hyperbolic functions or trigonometric functions, are rapidly derived. This method is applied to the Whitham–Broer–Kaup equation and a series of combinatorial solutions are obtained, showing that this method is a more concise and efficient approach and can uniformly construct many types of combined solutions to nonlinear partial differential equations.