Application of Binary Bell polynomial approach to a (2+1) dimensional nonlinear evolution equation

TL;DR

This paper employs the binary Bell polynomial method to analyze a (2+1)D nonlinear evolution equation, deriving its integrability features such as bilinear forms, Bäcklund transformations, Lax pairs, and conservation laws.

Contribution

It introduces a systematic binary Bell polynomial approach to derive integrability structures for a specific (2+1)D nonlinear PDE, expanding the method's applicability.

Findings

Derived bilinear formalism for the equation

Obtained Bäcklund transformation and Lax pair

Presented infinite conservation laws

Abstract

In this paper, we apply the binary Bell polynomial approach to a (2+1) dimensional nonlinear evolution equation. Namely, this study is an integrability work. Bilinear formalism, bilinear Backlund transformation, Lax pair of referred equation are obtained in the light of this work. Moreover, infinite conservation laws are also presented. This approach can also be applied to other nonlinear partial differential equations.