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 TMF, 2005, Volume 144, Number 2, Pages 313–323 (Mi tmf1856)

Multicomponent NLS-Type Equations on Symmetric Spaces and Their Reductions

V. S. Gerdjikova, G. G. Grahovskia, N. A. Kostovb

a Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences
b Institute of Electronics, Bulgarian Academy of Sciences

Abstract: We analyze the fundamental properties of models of the multicomponent nonlinear Schrodinger (NLS) type related to symmetric spaces and construct new types of reductions of these systems. We briefly describe the spectral properties of the Lax operators L, which in turn determine the corresponding recursion operator Ë and the fundamental properties of the relevant class of nonlinear evolution equations. The results are illustrated by specific examples of NLS-type systems related to the $\bold{DIII}$ symmetric space for the $so(8)$ algebra.

Keywords: multicomponent nonlinear Schrodinger equation, reduction group, symmetric spaces, Hamiltonian properties

DOI: https://doi.org/10.4213/tmf1856

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English version:
Theoretical and Mathematical Physics, 2005, 144:2, 1147–1156

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Citation: V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, “Multicomponent NLS-Type Equations on Symmetric Spaces and Their Reductions”, TMF, 144:2 (2005), 313–323; Theoret. and Math. Phys., 144:2 (2005), 1147–1156

Citation in format AMSBIB
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• https://doi.org/10.4213/tmf1856
• http://mi.mathnet.ru/eng/tmf/v144/i2/p313

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Kostov N.A., Atanasov V.A., Gerdjikov V.S., Grahovski G.G., “On the soliton solutions of the spinor Bose–Einstein condensate”, 14th International School on Quantum Electronics: Laser Physics and Applications, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 6604, 2007, T6041–T6041
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3. Zhou, RG, “An integrable decomposition of the symmetric matrix KdV equation”, Modern Physics Letters B, 22:13 (2008), 1307
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12. Grahovski G.G., “The Generalised Zakharov-Shabat System and the Gauge Group Action”, J. Math. Phys., 53:7 (2012), 073512
13. Han J., Yu J., He J., “A Matrix Lie Superalgebra and its Applications”, Adv. Math. Phys., 2013, 416520
14. Constantin A. Ivanov R., “Dressing Method for the Degasperis–Procesi Equation”, Stud. Appl. Math., 138:2 (2017), 205–226
15. V. S. Gerdjikov, “Kulish–Sklyanin-type models: Integrability and reductions”, Theoret. and Math. Phys., 192:2 (2017), 1097–1114
16. Gerdjikov V.S., “On Nonlocal Models of Kulish-Sklyanin Type and Generalized Fourier Transforms”, Advanced Computing in Industrial Mathematics, Studies in Computational Intelligence, 681, eds. Georgiev K., Todorov M., Georgiev I., Springer International Publishing Ag, 2017, 37–52
17. Gerdjikov V.S. Grahovski G.G. Ivanov R.I., “On Integrable Wave Interactions and Lax pairs on Symmetric Spaces”, Wave Motion, 71:SI (2017), 53–70
18. Caudrelier V., “Interplay Between the Inverse Scattering Method and Fokas'S Unified Transform With An Application”, Stud. Appl. Math., 140:1 (2018), 3–26
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