New Exact Solutions of Fractional Davey-Stewartson Equation with Power-Law Nonlinearity and New Integrable Davey-Stewartson Type Equation

Abstract

In this article, the Jacobi elliptic function method viz. mixed dn-sn method has been presented for finding the travelling wave solutions of the Davey-Stewartson Equations. As a result, some solitary wave solutions and doubly periodic solutions are obtained in terms of Jacobi elliptic functions. Moreover, solitary wave solutions are obtained as simple limits of doubly periodic functions. These solutions can be useful to explain some physical phenomena. The proposed Jacobi elliptic function method is efficient, powerful and can be used in order to establish more newly exact solutions for other kinds of nonlinear fractional partial differential equations arising in mathematical physics.