Bilinear approach to soliton and periodic wave solutions of two nonlinear evolution equations of Mathematical Physics

Abstract

Abstract In the present paper, the potential Kadomtsev–Petviashvili equation and ( 3+1 $3+1$)-dimensional potential-YTSF equation are investigated, which can be used to describe many mathematical and physical backgrounds, e.g., fluid dynamics and communications. Based on Hirota bilinear method, the bilinear equation for the ( 3+1 $3+1$)-dimensional potential-YTSF equation is obtained by applying an appropriate dependent variable transformation. Then N-soliton solutions of nonlinear evolution equation are derived by the perturbation technique, and the periodic wave solutions for potential Kadomtsev–Petviashvili equation and ( 3+1 $3+1$)-dimensional potential-YTSF equation are constructed by employing the Riemann theta function. Furthermore, the asymptotic properties of periodic wave solutions show that soliton solutions can be derived from periodic wave solutions.

Keywords

• Potential Kadomtsev–Petviashvili equation
• (3 + 1)-dimensional potential-YTSF equation
• N-soliton solution
• Periodic wave solution
• Hirota method