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A deformed reduced semi-discrete Kaup–Newell equation, the related integrable family and Darboux transformation

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  • Xu, Xi-Xiang

Abstract

A deformed reduced semi-discrete Kaup–Newell equation and its related integrable family are derived from discrete zero curvature equation. A Darboux transformation of Lax pair of this equation is established with the help of gauge transformation. By means of the resulting Darboux transformation, three exact solutions are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:275-283
    DOI: 10.1016/j.amc.2014.11.063
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    References listed on IDEAS

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    1. Yang, Hongxiang & Xu, Xixiang & Ding, Haiyong, 2005. "New hierarchies of integrable positive and negative lattice models and Darboux transformation," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1091-1103.
    2. Ma, Wen-Xiu & Maruno, Ken-ichi, 2004. "Complexiton solutions of the Toda lattice equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 219-237.
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    Cited by:

    1. 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.
    2. Wen-Xiu Ma, 2023. "Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions," Mathematics, MDPI, vol. 11(22), pages 1-9, November.
    3. Tongshuai Liu & Huanhe Dong, 2019. "The Prolongation Structure of the Modified Nonlinear Schrödinger Equation and Its Initial-Boundary Value Problem on the Half Line via the Riemann-Hilbert Approach," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    4. Shi, Yu-Ren & Yang, Xue-Ying & Tang, Na & Wang, Deng-Shan, 2018. "Effects of Zeeman field on the dynamical instability of flat states for spin-2 Bose–Einstein condensates in an optical lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 39-55.

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