Nonlinear wave behaviors for a combined Kadomtsev-Petviashvili-Boiti-Leon-Manna-Pempinelli equation in fluid dynamics, plasma physics and nonlinear optics

Research in real-world applications has been driving the progress of nonlinear science, with fluid dynamics and plasma physics currently capturing significant attention. This paper explores newly proposed (2+1)-dimensional nonlinear wave equation, combining the Kadomtsev-Petviashvili (KPE) and Boiti-Leon-Manna-Pempinelli equations (BLMPE). The equation, which includes nonlinear and dispersive terms, has potential applications in fluid dynamics, plasma physics, nonlinear optics, and geophysical flows. We analyze its integrability, showing that does not satisfy the Painlev & eacute; property but admits multi-soliton solutions. Using the Hirota bilinear approach and extended homoclinic test approach, we derive analytic solutions such as lump waves, soliton interactions, and breather waves, with the latter leading to rogue wave formation.