A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms

Інший ID: 2010 Mathematics Subject Classification: 37K15; 39A14; 70H06

URI: http://dspace.nbuv.gov.ua/handle/123456789/147391

Посилання: A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms / M.C. Hay // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 15 назв. — англ.

Підтримка: This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html. The author appreciatively acknowledges support from the Global COE Program “Education and Research Hub for Mathematics-for-Industry” from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

Дата: 2011

Завантажень: 256

A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms

Анотація:

We expand the completeness study instigated in [J. Math. Phys. 50 (2009), 103516, 29 pages] which found all 2×2 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.

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