Breather-wave, periodic-wave and traveling-wave solutions for a (2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation for an incompressible fluid

In this paper, the investigation is conducted on a (2 + 1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation for an incompressible fluid. Via the Riemann theta function, periodic-wave solutions are derived, and breather-wave solutions are constructed with the aid of the extended homoclinic test approach. Based on the polynomial expansion method, several traveling-wave solutions are derived. Besides, we observe that the amplitude of the breather keeps unchanged during the propagation and the traveling wave which is kink shaped propagates stably. Furthermore, we analyze the transition between the periodic-wave and soliton solutions, which implies that the periodic-wave solutions tend to the soliton solutions via a limiting procedure.

Automated summary

In this paper, an investigation is conducted on a (2 + 1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation for an incompressible fluid. Periodic-wave solutions and breather-wave solutions are derived, and several traveling-wave solutions are obtained. Additionally, the amplitude of the breather remains unchanged during propagation, and the kink-shaped traveling wave propagates stably. Moreover, the transition between periodic-wave and soliton solutions is analyzed, showing that periodic-wave solutions tend towards soliton solutions through a limiting procedure.