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Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type
Інший ID:
2000 Mathematics Subject Classification: 37K20; 35Q51; 74J30; 78A60
Посилання:
Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type / V.S. Gerdjikov, N.A. Kostov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). It is our pleasure to thank Professor Gaetano Vilasi for useful discussions. One of us (VSG) thanks the Physics Department of the University of Salerno for the kind hospitality and the Italian Istituto Nazionale di Fisica Nucleare for financial support. We also thank the Bulgarian Science Foundation for partial support through contract No. F-1410. One of us (VSG) is grateful to the organizers of the Kyiv conference for their hospitality and acknowledges financial support by an CEI grant.
Дата:
2008
Переглядів:
453
Завантажень:
229
Анотація:
New reductions for the multicomponent modified Korteweg-de Vries (MMKdV) equations on the symmetric spaces of DIII-type are derived using the approach based on the reduction group introduced by A.V. Mikhailov. The relevant inverse scattering problem is studied and reduced to a Riemann-Hilbert problem. The minimal sets of scattering data Ti, i = 1, 2 which allow one to reconstruct uniquely both the scattering matrix and the potential of the Lax operator are defined. The effect of the new reductions on the hierarchy of Hamiltonian structures of MMKdV and on Ti are studied. We illustrate our results by the MMKdV equations related to the algebra g @ so(8) and derive several new MMKdV-type equations using group of reductions isomorphic to Z₂, Z₃, Z₄.
