Exact solutions to the space–time fractional shallow water wave equation via the complete discrimination system for polynomial method

Abstract

The work of this article is to transform the famous nonlinear space–time fractional shallow water wave equations, namely coupled Korteweg-de Vries equations into ordinary differential equations via the complex fractional traveling wave transformation, and find the exact solutions through the complete discrimination system for polynomial method. At the same time, we build the appropriate example for the identified parameters to show the existence of each solution. Besides, providing a direct perspective to show that our solutions do exist by the three-dimensional and two-dimensional graphics.