Abundant solitons for the generalized Hirota–Satsuma couple KdV system with an efficient technique

Abstract

The generalized Hirota–Satsuma Coupled Kortwedge–de Varies (GHSC–KdV) system is considered for investigation to study the exact solutions by using the extended generalized G′/G-expansion technique. The GHSC–KdV system describes the interaction of two long waves with different dispersion relations. The dynamical structures of the obtained solutions are solitary-type waves, multi-soliton waves, and singular–kink type waves. It contains information about the hyperbolic, trigonometric, and rational function solutions for the above system. Furthermore, the derived solutions of the system that comprises arbitrary functional parameters and other constant parameters can be used to enhance the advanced behavior of physical situations.