On nonclassical symmetries, Painlevé analysis and singular, periodic and solitary wave solutions of generalized Hirota-Satsuma coupled KdV system

Abstract

In this work, we investigate the generalized Hirota-Satsuma coupled KdV system which is materialized in the theory of shallow water waves. Nonclassical symmetries of governing system are derived using Bluman and Cole method. The obtained symmetries are in the form of Jacobi elliptic functions, which are more generalized than earlier obtained symmetries for the governing system. Some new singular, periodic and solitary wave solutions of the governing system are also derived by assuming the Jacobi elliptic function type solutions. The obtained exact solutions for the considered system are verified by graphical representation. The Painlevé property of the considered system is also checked with the help of Kruksal’s method and symbolic computational tool Maple which shows the integrable behaviour of the considered system.