Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type

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 proble...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2008
Main Authors: Gerdjikov, V.S., Kostov, N.A.
Format: Article
Language:English
Published: Інститут математики НАН України 2008
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149036
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary: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.
ISSN:1815-0659