Explicit solutions for the coupled nonlinear Drinfeld–Sokolov–Satsuma–Hirota system

Abstract

In this paper, we firstly solve the auxiliary elliptic equation and obtain the explicit solutions to the equation. Then, by the modified polynomial expansion method, we obtain more new explicit solutions for the coupled nonlinear Drinfeld–Sokolov–Satsuma–Hirota system, and we get the figures of the solutions with special parameters. There exist mainly three types of solutions for the system: trigonometric function traveling wave solutions, hyperbolic function traveling wave solutions, and rational function traveling wave solutions. From physics, the solutions are compacton, soliton, cuspon, and peakon traveling waves.

Keywords

• Drinfeld–Sokolov–Satsuma–Hirota system
• Partial differential equation
• Elliptic equation
• Modified polynomial expansion methods
• Explicit solutions