Geodesic
Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type
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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 $\mathcal T_i$, $i=1,2$ 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 $\mathbb Z_2$, $\mathbb Z_3$, $\mathbb Z_4$.
Keywords: multicomponent modified Korteweg–de Vries (MMKdV) equations; reduction group; Riemann–Hilbert problem; Hamiltonian structures. 
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     title = {Reductions of {Multicomponent} {mKdV} {Equations} on {Symmetric} {Spaces} of {DIII-Type}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a28/}
}
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Vladimir S. Gerdjikov; Nikolay A. Kostov. Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a28/

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