Phase portraits and new exact traveling wave solutions of the (2+1)-dimensional Hirota system

Abstract

In this paper, we investigate the (2+1)-dimensional Hirota system of equations, which is essential for modeling physical events since it contains the NLS equation and the cmKdV equation. We apply the Jacobi elliptic function method to obtain new results. By using some ansatz in terms of finite Jacobi elliptic functions, we have obtained various exact solutions, such as dark solitons, bright solitons, and periodic solutions. Moreover, for some reductions as α=0,β=1 and α=1,β=0, we obtain the exact solutions for the (2+1)-dimensional NLS equation and the (2+1)-dimensional cmKdV equation. The dynamics of the obtained solutions are presented in the figures. We also analyze the phase portraits of the (2+1)-dimensional Hirota system.

Keywords

• (2+1)-dimensional Hirota system
• Periodic wave
• Soliton
• Traveling wave
• Phase portraits