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 sechp function, we obtain exact bright soliton solutions and another wave ansatz in the form of tanhp 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