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Teoreticheskaya i Matematicheskaya Fizika, 2017, Volume 192, Number 2, Pages 187–206
DOI: https://doi.org/10.4213/tmf9319
(Mi tmf9319)
 

This article is cited in 11 scientific papers (total in 11 papers)

Kulish–Sklyanin-type models: Integrability and reductions

V. S. Gerdjikovabc

a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
b Institute for Advanced Physical Studies, New Bulgarian University, Sofia, Bulgaria
c Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
References:
Abstract: We start with a Riemann–Hilbert problem (RHP) related to BD.I-type symmetric spaces $SO(2r+1)/S(O(2r-2s+1)\otimes O(2s))$, $s\ge1$. We consider two RHPs: the first is formulated on the real axis $\mathbb R$ in the complex-$\lambda$ plane; the second, on $\mathbb R\oplus i\mathbb R$. The first RHP for $s=1$ allows solving the Kulish–Sklyanin (KS) model; the second RHP is related to a new type of KS model. We consider an important example of nontrivial deep reductions of the KS model and show its effect on the scattering matrix. In particular, we obtain new two-component nonlinear Schrödinger equations. Finally, using the Wronski relations, we show that the inverse scattering method for KS models can be understood as generalized Fourier transforms. We thus find a way to characterize all the fundamental properties of KS models including the hierarchy of equations and the hierarchy of their Hamiltonian structures.
Keywords: symmetric space, multicomponent nonlinear Schrödinger equation, Lax representation, reduction group.
Received: 15.12.2016
Revised: 06.02.2017
English version:
Theoretical and Mathematical Physics, 2017, Volume 192, Issue 2, Pages 1097–1114
DOI: https://doi.org/10.1134/S0040577917080013
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. S. Gerdjikov, “Kulish–Sklyanin-type models: Integrability and reductions”, TMF, 192:2 (2017), 187–206; Theoret. and Math. Phys., 192:2 (2017), 1097–1114
Citation in format AMSBIB
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\paper Kulish--Sklyanin-type models: Integrability and reductions
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\pages 1097--1114
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  • https://doi.org/10.4213/tmf9319
  • https://www.mathnet.ru/eng/tmf/v192/i2/p187
  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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