Lax pair and lump solutions for the (2+1)-dimensional DJKM equation associated with bilinear Bäcklund transformations

  • Li Cheng
  • Yi Zhang
  • Mei-Juan Lin


We aim to explore exact solutions and integrable properties to the (2+1)-dimensional DJKM equation. Based on the bilinear Bäcklund transformation, we first furnish Lax pair and complex exponential wave function solutions, and then give complexitons or hyperbolic function solutions. Moreover, via the nonlinear superposition formula, the construction procedure for presenting rational solutions is improved. The key step is that all the involved parameters are extended to the complex field. In particular, we show that the (2+1)-dimensional DJKM equation possesses a general class of lump solutions when \({\sigma }^2=-1\).


DJKM equation Bäcklund transformation Lax pair Complexiton Lump solution 

Mathematics Subject Classification

35Q51 35Q53 37K40 



The authors express their sincere thanks to the referees and editors for their valuable comments.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Normal SchoolJinhua PolytechnicJinhuaChina
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaChina

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