2007/07/05 by Hai-Qiang Zhang, Zhang, Hai-Qiang, Juan Li +8
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Numerical methods for differential equations #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.0707.0787
arxiv created 2007/07/05 · openalex publication_date 2007/07/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.