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Construction of solutions for an integrable differential-difference equation by Darboux–Bäcklund transformation

Author

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  • Lu, Rong-Wu
  • Xu, Xi-Xiang
  • Zhang, Ning

Abstract

We first establish a one-fold Darboux–Bäcklund transformation for the integrable differential-difference equation which is presented in Ref. [6] by means of a proper gauge transformation matrix. Then, as a result of the N times one-fold Darboux–Bäcklund transformation, we derive N-fold Darboux–Bäcklund transformation. Finally, using the obtained Darboux–Bäcklund transformation, two exact solutions are worked out.

Suggested Citation

  • Lu, Rong-Wu & Xu, Xi-Xiang & Zhang, Ning, 2019. "Construction of solutions for an integrable differential-difference equation by Darboux–Bäcklund transformation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 389-397.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:389-397
    DOI: 10.1016/j.amc.2019.05.049
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    References listed on IDEAS

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    1. Xu, Xi-Xiang, 2015. "A deformed reduced semi-discrete Kaup–Newell equation, the related integrable family and Darboux transformation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 275-283.
    2. Xi-Xiang Xu & Meng Xu, 2018. "A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-11, June.
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