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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 089, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.089 (Mi sigma647) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A Completeness Study on Certain $2\times2$ Lax Pairs Including Zero Terms

Mike C. Hay

Institute of Mathematics for Industry, Kyushu University, Ito Campus, 744 motooka, nishi-ku, Fukuoka, 819-0395, Japan
Full-text PDF (349 kB) Citations (5)
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DOI: https://doi.org/10.3842/SIGMA.2011.089
Abstract: We expand the completeness study instigated in [J. Math. Phys. 50 (2009), 103516, 29 pages] which found all $2\times2$ Lax pairs with non-zero, separable terms in each entry of each Lax matrix, along with the most general nonlinear systems that can be associated with them. Here we allow some of the terms within the Lax matrices to be zero. We cover all possible Lax pairs of this type and find a new third order equation that can be reduced to special cases of the non-autonomous lattice KdV and lattice modified KdV equations among others.
Keywords: discrete integrable systems; Lax pairs.
Received: April 9, 2011; in final form September 4, 2011; Published online September 14, 2011
Bibliographic databases:
Document Type: Article
MSC: 37K15; 39A14; 70H06
Language: English
Citation: Mike C. Hay, “A Completeness Study on Certain $2\times2$ Lax Pairs Including Zero Terms”, SIGMA, 7 (2011), 089, 12 pp.
Citation in format AMSBIB
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\paper A Completeness Study on Certain $2\times2$ Lax Pairs Including Zero Terms
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\vol 7
\papernumber 089
\totalpages 12
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    • This publication is cited in the following 5 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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