An Exp-function method for new NN-soliton solutions with arbitrary functions of a (2+1)(2+1)-dimensional vcBK system

In this paper, the Exp-function method is generalized to construct NN-soliton solutions of the (2+1)-dimensional variable-coefficient Broer–Kaup (vcBK) system. As a result, new and more general 1-soliton, 2-soliton and 3-soliton solutions with arbitrary functions are obtained, from which the uniform formulae of NN-soliton solutions are derived. Based on one of the obtained 2-soliton solution, the fission and fusion phenomena between the peakons and solitary waves are investigated. It is shown that the Exp-function method may provide us with a straightforward, effective and alternative mathematical tool for generating NN-soliton solutions of nonlinear evolution equations in mathematical physics.