# Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type - Nonlinear Sciences > Exactly Solvable and Integrable Systems

Abstract: New reductions for the multicomponent modified Korteveg-de Vries MMKdVequations on the symmetric spaces of {\bf DIII}-type are derived using theapproach based on the reduction group introduced by A.V. Mikhailov. Therelevant inverse scattering problem is studied and reduced to a Riemann-Hilbertproblem. The minimal sets of scattering data $\mathcal{T} i$, $i=1,2$ whichallow one to reconstruct uniquely both the scattering matrix and the potentialof the Lax operator are defined. The effect of the new reductions on thehierarchy of Hamiltonian structures of MMKdV and on $\mathcal{T} i$ arestudied. We illustrate our results by the MMKdV equations related to thealgebra $\mathfrak{g}\simeq so8$ and derive several new MMKdV-type equationsusing group of reductions isomorphic to ${\mathbb Z} {2}$, ${\mathbb Z} {3}$,${\mathbb Z} {4}$.

Author: Vladimir S. Gerdjikov, Nikolay A. Kostov

Source: https://arxiv.org/