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A Darboux transformation for the Volterra lattice equation

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Abstract

A Darboux transformation is presented for the Volterra lattice equation, based on a pair of \(2\times 2\) matrix spectral problems. The resulting DT is applied to construction of solitary wave solutions from a constant seed solution. A particular phenomenon is that only one condition is required in determining the corresponding Darboux matrix, but not two as for most pairs of \(2\times 2 \) matrix spectral problems.

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Acknowledgements

The work was supported in part by NSFC under the Grants 11301454, 11301331, 11371086, 11571079 and 51771083, NSF under the Grant DMS-1664561, the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17KJB110020), Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT under Grant No. 2017XKZD11, and the Distinguished Professorships by Shanghai University of Electric Power, China and North-West University, South Africa.

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Authors and Affiliations

  1. College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai, 200090, China

    Wen-Xiu Ma

  2. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    Wen-Xiu Ma

  3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA

    Wen-Xiu Ma

  4. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Wen-Xiu Ma

  5. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China

    Wen-Xiu Ma

  6. Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Mmabatho, 2735, South Africa

    Wen-Xiu Ma

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Ma, WX. A Darboux transformation for the Volterra lattice equation. Anal.Math.Phys. 9, 1711–1718 (2019). https://doi.org/10.1007/s13324-018-0267-z

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  • DOI: https://doi.org/10.1007/s13324-018-0267-z

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