In terms of the invariant subspace method and under the assumption that the dimension of invariant subspace is two, a number of two-dimensional invariant subspaces are obtained and a series of different separation of variables solutions are given correspondingly. At the same time, the symbolic solving algorithm is given based on the symbolic computation system Maple such that the method can be easily extended from low dimension to high dimension cases.

invariant subspace; nonlinear partial differential equations; generalized separation of variables solutions; symbolic computation