Analytical solutions to the M-derivative resonant Davey-Stewartson equations

Abstract

In this paper, the (2 + 1)-dimensional resonant Davey-Stewartson equations are solved by using two methods; namely, (m + 1G')-expansion and (m + G'/G)-expansion methods. A wave transform is used to convert the (2+1)-dimensional resonant Davey-Stewartson (RDS) equations with M-derivative into a system of nonlinear ordinary differential equations. Different forms of solutions, such as dark, bright, singular and periodic singular solutions are successfully constructed. The obtained solutions are plotted in 3D for both M-derivative and classical derivative to more understand the effect of M-derivative on the studied equation.