reductions of multicomponent mkdv equations on symmetric spaces of diii-type

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ID: 246243
2008
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Abstract
New reductions for the multicomponent modified Korteweg-de Vries (MMKdV) equations on the symmetric spaces of {f 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 $mathcal{T}_i$, $i=1,2$ 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 $mathcal{T}_i$ are studied. We illustrate our results by the MMKdV equations related to the algebra $mathfrak{g}simeq so(8)$ and derive several new MMKdV-type equations using group of reductions isomorphic to ${mathbb Z}_{2}$, ${mathbb Z}_{3}$, ${mathbb Z}_{4}$.
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kostov2008symmetry,reductions Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Nikolay A. Kostov;Vladimir S. Gerdjikov
Journal Therapeutic drug monitoring
Year 2008
DOI
DOI not found
URL
http://dx.doi.org/10.3842/SIGMA.2008.029
Keywords
riemann-hilbert problem

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