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

Abstract

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 \({\sigma }^2=-1\).

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

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Correspondence to Li Cheng.

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Cheng, L., Zhang, Y. & Lin, M. Lax pair and lump solutions for the (2+1)-dimensional DJKM equation associated with bilinear Bäcklund transformations. Anal.Math.Phys. 9, 1741–1752 (2019). https://doi.org/10.1007/s13324-018-0271-3

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Keywords

  • DJKM equation
  • Bäcklund transformation
  • Lax pair
  • Complexiton
  • Lump solution

Mathematics Subject Classification

  • 35Q51
  • 35Q53
  • 37K40