Exploring nonlinear wave dynamics through an extended (2+1)-dimensional nonlinear evolution equation: Integrability and pfaffian solutions

Abstract

This paper introduces a generalized (2+1)-dimensional nonlinear evolution equation, extending the classical Hirota bilinear framework to investigate novel aspects of nonlinear wave dynamics. By employing a combination of the Hirota bilinear method and the Pfaffian formulation, we systematically derive a rich variety of exact solutions, including multi-soliton waves, breathers, lump, periodic solutions, and complex hybrid structures. The study also examines the integrability of the proposed model, revealing that despite failing the Painlev & eacute; test, the equation admits integrability in the solitonic sense. The results highlight the model's broad adaptability and its promise for use in diverse scientific fields, including nonlinear optical systems, fluid dynamics, and plasma research.