A Darboux transformation for the Volterra lattice equation

  • Wen-Xiu MaEmail author


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.


Matrix spectral problem Integrable lattice equation Darboux transformation 

Mathematics Subject Classification

35Q51 35Q53 37K40 



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.

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interest.


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Authors and Affiliations

  1. 1.College of Mathematics and PhysicsShanghai University of Electric PowerShanghaiChina
  2. 2.Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA
  4. 4.Department of MathematicsZhejiang Normal UniversityJinhuaChina
  5. 5.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoChina
  6. 6.Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical ModellingNorth-West UniversityMmabathoSouth Africa

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