2008/03/11 by Vladimir S. Gerdjikov, Nikolay A. Kostov · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI
paper · pdf · doi:10.3842/sigma.2008.029
published as SIGMA 4 (2008), 029, 30 pages · This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2008/03/11 · openalex publication_date 2008/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 T i are studied. We illustrate our results by the MMKdV equations related to the algebra g so(