Variable-coefficient hyperbola function method and its application to (2+1)-dimensional variable-coefficient Broer-Kaup system

Based on a new intermediate transformation, a variable-coefficient hyperbola function method is proposed. Being concise and straightforward, it is applied to the (2+1)-dimensional variable-coefficient Broer Kaup system. As a result, several new families of exact soliton-like solutions are obtained, besides the travelling wave. When imposing some conditions on them, the new exact solitary wave solutions of the (2+1)-dimensional Broer-Kaup system are given. The method can be applied to other variable-coefficient nonlinear evolution equations in mathematical physics.