Evolution of complex waves via Davey-Stewartson equation

Davey-Stewartson equations (DSEs) have been discussed to examine the features of wave motion in finite depth water which is affected by gravitational force and surface tension. The new versions of the generalized F-expansion method and the generalized -expansion method are suggested to evaluate the analytical solutions of the DSEs. Thus, single, combined and mixed non-degenerative Jacobi elliptic function solutions (JEFSs) and degenerative solutions of the DSEs are obtained to contribute to the literature. These wave solutions are fresh and unexplored. The visual representations of some solutions are also shown in three and two dimensions.