Bright and Dark Soliton Solutions of the (2 + 1)-Dimensional Evolution Equations

Abstract

In this paper, we obtained the 1-soliton solutions of the (2+1)-dimensional Boussinesq equation and the Camassa–Holm–KP equation. By using a solitary wave ansatz in the form of sech^p function, we obtain exact bright soliton solutions and another wave ansatz in the form of tanh^p function we obtain exact dark soliton solutions for these equations. The physical parameters in the soliton solutions are obtained nonlinear equations with constant coefficients.

Keywords:

• exact solutions
• bright and dark solitons
• Boussinesq equation
• Camassa–Holm–KP equation

AMS Subject Classification:

• 35C08
• 35Q51
• 35Q68
• 37K40