A general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method, and the extended auxiliary function method with computerized symbolic computation is proposed to construct more new exact solutions for coupled Schrödinger-Boussinesq equations. As a result, several families of new generalized Jacobi elliptic function wave solutions are obtained by using this method, some of them are degenerated to solitary wave solutions and trigonometric function solutions in the limited cases, which shows that the general method is more powerful than plenty of traditional methods and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.
"New Exact Jacobi Elliptic Function Solutions for the Coupled Schrödinger-Boussinesq Equations." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/170835