Multiple exp-function method to solve the nonlinear space–time fractional partial differential symmetric regularized long wave (SRLW) equation and the (1+1)-dimensional Benjamin–Ono equation

Abstract

In this study, we apply relatively analytical techniques, the multiple [Formula: see text]-function method, [Formula: see text]-function method and [Formula: see text]-expansion method to get approximate and analytic solutions of some nonlinear partial differential equations (PDEs), i.e., the nonlinear space–time fractional partial differential symmetric regularized long wave equation, an impressive model to characterize ion-acoustic and space change waves, the nonlinear [Formula: see text]-dimensional Fokas PDE, a meaningful multi-dimensional extension of the Kadomtsev–Petviashvili (KP) and Davey–Stewartson (DS) equations, [Formula: see text]-dimensional Bateman–Burgers equation, a simplification of a more complex and sophisticated model, and the [Formula: see text]-dimensional Benjamin–Ono equation, a model for the propagation of unidirectional internal waves in stratified fluids. Finally, we propose the numerical results in tables and discuss advantages and disadvantages of the mentioned methods.