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Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation

Received: 14 September 2014     Accepted: 29 September 2014     Published: 10 October 2014
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Abstract

An integrable coupling of the known integrable differential-difference equation and its Lax pair are presented. Based on the gauge transformation between the corresponding four-by- four matrix spectral problems, a Darboux transformation of Lax pair for the integrable coupling is established. As an application of the obtained Darboux transformation, an explicit solution is given.

Published in Applied and Computational Mathematics (Volume 3, Issue 5)
DOI 10.11648/j.acm.20140305.18
Page(s) 240-246
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Integrable Differential-Difference Equation, Integrable Coupling, Darboux, Transformation, Explicit Solution

References
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  • APA Style

    Xi-Xiang Xu. (2014). Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation. Applied and Computational Mathematics, 3(5), 240-246. https://doi.org/10.11648/j.acm.20140305.18

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    ACS Style

    Xi-Xiang Xu. Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation. Appl. Comput. Math. 2014, 3(5), 240-246. doi: 10.11648/j.acm.20140305.18

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    AMA Style

    Xi-Xiang Xu. Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation. Appl Comput Math. 2014;3(5):240-246. doi: 10.11648/j.acm.20140305.18

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  • @article{10.11648/j.acm.20140305.18,
      author = {Xi-Xiang Xu},
      title = {Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {5},
      pages = {240-246},
      doi = {10.11648/j.acm.20140305.18},
      url = {https://doi.org/10.11648/j.acm.20140305.18},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.18},
      abstract = {An integrable coupling of the known integrable differential-difference equation and its Lax pair are presented. Based on the gauge transformation between the corresponding four-by- four matrix spectral problems, a Darboux transformation of Lax pair for the integrable coupling is established. As an application of the obtained Darboux transformation, an explicit solution is given.},
     year = {2014}
    }
    

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    AB  - An integrable coupling of the known integrable differential-difference equation and its Lax pair are presented. Based on the gauge transformation between the corresponding four-by- four matrix spectral problems, a Darboux transformation of Lax pair for the integrable coupling is established. As an application of the obtained Darboux transformation, an explicit solution is given.
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Author Information
  • College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

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