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Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries
Інший ID:
2010 Mathematics Subject Classification: 37K10; 51M05; 51B10
DOI: http://dx.doi.org/10.3842/SIGMA.2013.001
DOI: http://dx.doi.org/10.3842/SIGMA.2013.001
Посилання:
Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries / C. Qu, J. Song, R. Yao // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 60 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html.
The authors would like to thank the anonymous referees for constructive suggestions and comments. This work was supported by the China NSF for Distinguished Young Scholars under Grant 10925104 and the China NSF under Grants 11071278 and 60970054.
Дата:
2013
Переглядів:
508
Завантажень:
237
Анотація:
In this paper, multi-component generalizations to the Camassa-Holm equation, the modified Camassa-Holm equation with cubic nonlinearity are introduced. Geometric formulations to the dual version of the Schrödinger equation, the complex Camassa-Holm equation and the multi-component modified Camassa-Holm equation are provided. It is shown that these equations arise from non-streching invariant curve flows respectively in the three-dimensional Euclidean geometry, the two-dimensional Möbius sphere and n-dimensional sphere Sn(1). Integrability to these systems is also studied.
