Solitary and traveling wave solutions for the Davey–Stewartson equation using the Jacobi elliptic function expansion method

Abstract

In our paper we modify the Jacobi elliptic function expansion method to obtain solutions to the Davey–Stewartson system of equations. Two categories of nonsingular solutions are obtained for both traveling and solitary waves and both with and without chirp. In both cases there is an arbitrary term in the mean flow field, meaning one can obtain solutions for arbitrary forms of the mean flow field.