Symbolic-computation study of integrable properties for the (2+1)-dimensional Gardner equation with the two-singular-manifold method

TL;DR

This paper applies the two-singular-manifold method to analyze the integrable properties of the (2+1)-dimensional Gardner equation, deriving key structures like Lax pairs, transformations, and solutions using symbolic computation.

Contribution

It introduces a symbolic-computation approach to derive integrable structures for the (2+1)-dimensional Gardner equation using the two-singular-manifold method.

Findings

Derived Hirota bilinear form and Bäcklund transformation.

Constructed Lax pairs and Darboux transformation.

Obtained N-soliton Grammian solutions through symbolic computation.

Abstract

The singular manifold method from the Painleve analysis can be used to investigate many important integrable properties for the nonlinear partial differential equations.In this paper, the two-singular-manifold method is applied to the (2+1)-dimensional Gardner equation with two Painleve expansion branches to determine the Hirota bilinear form, Backlund transformation, Lax pairs and Darboux transformation. Based on the obtained Lax pairs, the binary Darboux transformation is constructed and the N N Grammian solution is also derived by performing the iterative algorithm Ntimes with symbolic computation.