Non-Travelling Wave Solutions of the (2+1)-Dimensional Dispersive Long Wave System

It is important to seek for more explicit exact solutions of nonlinear partial differential equations (NLPDEs) in mathematical physics. With the help of symbolic computation software like Maple or Mathematica, much work has been focused on the various extensions and applications of the known methods to construct exact solutions of NLPDEs. Mathematical modelling of physical systems often leads to nonlinear evolution equations (NLEEs). The study of (2+1)-dimensionalNLEEs, or even higher dimensional NLEEs, has also attracted more attention. There are many powerful and direct methods to construct the exact solutions of NLPDEs, such as the inverse scattering transform [1], tanh-function method [2 – 4], the generalized hyperbolic function method [5, 6], Exp-function method [7], sine/cosine method [8] and so on. Recently, many exact solutions expressed by Jacobi elliptic functions (JEFs) of NLEEs have been obtained by Jacobi elliptic function expansion method [9 – 11], mapping method [12, 13], F-expansion method [14], the extended F-expansion method [15], the improved generalized F-expansion method [16, 17], the generalized Jacobi elliptic function method [18, 19], the variable-coefficient F-expansion method [20] and other methods [21 – 23]. The F-expansion method [14] is an over-all generalization of Jacobi elliptic function expansion method. Using many methods [3 – 6, 9 – 11, 14, 15, 22, 23], we can get only the travelling wave solutions. Ren and Zhang [16] and Zhang and Xia [17]