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

This article is cited in 18 scientific papers (total in 18 papers)

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 Л 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

Full text: PDF file (255 kB)
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English version:
Theoretical and Mathematical Physics, 2005, 144:2, 1147–1156

Bibliographic databases:


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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    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  isi
    2. Atanasov, VA, “Fordy-Kulish model and spinor Bose–Einstein condensate”, Journal of Nonlinear Mathematical Physics, 15:3 (2008), 291  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Zhou, RG, “An integrable decomposition of the symmetric matrix KdV equation”, Modern Physics Letters B, 22:13 (2008), 1307  crossref  zmath  adsnasa  isi  elib  scopus  scopus
    4. Gerdjikov, VS, “Solutions of multi-component NLS models and Spinor Bose–Einstein condensates”, Physica D-Nonlinear Phenomena, 238:15 (2009), 1306  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. V. S. Gerdjikov, G. G. Grahovski, “Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory”, SIGMA, 6 (2010), 044, 29 pp.  mathnet  crossref  mathscinet
    6. Aristophanes Dimakis, Folkert Müller-Hoissen, “Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions”, SIGMA, 6 (2010), 055, 27 pp.  mathnet  crossref  mathscinet
    7. Gerdjikov V.S., Grahovski G.G., “Two Soliton Interactions of BD.I Multicomponent NLS Equations and Their Gauge Equivalent”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1301, 2010, 561–572  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Constantin A., Ivanov R.I., Lenells J., “Inverse scattering transform for the Degasperis–Procesi equation”, Nonlinearity, 23:10 (2010), 2559–2575  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    9. Gerdjikov V.S., “On Soliton Interactions of Vector Nonlinear Schrodinger Equations”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1404, 2011  isi
    10. Sonnier W.J., “Repelling, Delay, and Polarization for Soliton Collisions in the CNLSE”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1404, 2011  isi
    11. Sonnier W.J., “Dynamics of repelling soliton collisions in coupled Schrodinger equations”, Wave Motion, 48:8 (2011), 805–813  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Grahovski G.G., “The Generalised Zakharov-Shabat System and the Gauge Group Action”, J. Math. Phys., 53:7 (2012), 073512  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. Han J., Yu J., He J., “A Matrix Lie Superalgebra and its Applications”, Adv. Math. Phys., 2013, 416520  crossref  mathscinet  zmath  isi  scopus  scopus
    14. Constantin A. Ivanov R., “Dressing Method for the Degasperis–Procesi Equation”, Stud. Appl. Math., 138:2 (2017), 205–226  crossref  mathscinet  zmath  isi  scopus
    15. V. S. Gerdjikov, “Kulish–Sklyanin-type models: Integrability and reductions”, Theoret. and Math. Phys., 192:2 (2017), 1097–1114  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    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  crossref  mathscinet  isi  scopus  scopus
    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  crossref  mathscinet  isi  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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