Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation
Applied and Computational Mathematics
Volume 3, Issue 5, October 2014, Pages: 240-246
Received: Sep. 14, 2014; Accepted: Sep. 29, 2014; Published: Oct. 10, 2014
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Author
Xi-Xiang Xu, College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China
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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.
Keywords
Integrable Differential-Difference Equation, Integrable Coupling, Darboux, Transformation, Explicit Solution
To cite this article
Xi-Xiang Xu, Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation, Applied and Computational Mathematics. Vol. 3, No. 5, 2014, pp. 240-246. doi: 10.11648/j.acm.20140305.18
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