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

Xi-Xiang Xu

doi:doi:10.11648/j.acm.20140305.18

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

Xi-Xiang Xu

Published in Applied and Computational Mathematics (Volume 3, Issue 5)

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

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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},
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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.},
 year = {2014}
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TY  - JOUR
T1  - Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation
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PY  - 2014
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Author Information

Xi-Xiang Xu

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation
AU  - Xi-Xiang Xu
Y1  - 2014/10/10
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.18
DO  - 10.11648/j.acm.20140305.18
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 240
EP  - 246
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.18
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.
VL  - 3
IS  - 5
ER  -

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