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TMF, 2007, Volume 151, Number 3, Pages 391–404 (Mi tmf6054)  

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

$N$-soliton train and generalized complex Toda chain for the Manakov system

V. S. Gerdjikova, E. V. Doktorovb, N. P. Matsukac

a Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences
b B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus
c Institute of Mathematics, National Academy of Sciences of the Republic of Belarus

Abstract: We analyze the dynamical behavior of the $N$-soliton train of the Manakov system and of the vector NLS equation in the adiabatic approximation. We prove that the dynamics of the $N$-soliton train in both cases are described by a generalized version of the complex Toda chain model. This fact can be used to predict the asymptotic regimes of the $N$-soliton train provided the initial soliton parameters are given.

Keywords: complex Toda chain, Manakov model, adiabatic dynamics, vector soliton train

DOI: https://doi.org/10.4213/tmf6054

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English version:
Theoretical and Mathematical Physics, 2007, 151:3, 762–773

Bibliographic databases:


Citation: V. S. Gerdjikov, E. V. Doktorov, N. P. Matsuka, “$N$-soliton train and generalized complex Toda chain for the Manakov system”, TMF, 151:3 (2007), 391–404; Theoret. and Math. Phys., 151:3 (2007), 762–773

Citation in format AMSBIB
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\vol 151
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\pages 391--404
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Novoa D., Malomed B.A., Michinel H., Pérez-García V.M., “Supersolitons: Solitonic excitations in atomic soliton chains”, Phys. Rev. Lett., 101:14 (2008), 144101, 4 pp.  crossref  adsnasa  isi  scopus
    2. Doktorov E.V., Molchan M.A., “Soliton train dynamics in a weakly nonlocal non-Kerr nonlinear medium”, J. Phys. A, 41:31 (2008), 315101, 13 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Gerdjikov V.S., Kostov N.A., Doktorov E.V., Matsuka N.P., “Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose–Einstein mixtures”, Math. Comput. Simulation, 80:1 (2009), 112–119  crossref  mathscinet  zmath  isi  elib  scopus
    4. Janutka A., “Stability of multicomponent-soliton trains”, Phys Scripta, 82:4 (2010), 045001  crossref  zmath  adsnasa  isi  scopus
    5. Sonnier W.J., “Dynamics of repelling soliton collisions in coupled Schrodinger equations”, Wave Motion, 48:8 (2011), 805–813  crossref  mathscinet  zmath  isi  scopus
    6. Gerdjikov V.S., Todorov M.D., “On the Effects of Sech-Like Potentials on Manakov Solitons”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1561, ed. Todorov M., Amer Inst Physics, 2013, 75–83  crossref  adsnasa  isi  scopus
    7. Todorov M.D., Gerdjikov V.S., Kyuldjiev A.V., “Modeling Interactions of Soliton Trains. Effects of External Potentials”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1629, ed. Todorov M., Amer Inst Physics, 2014, 186–200  crossref  mathscinet  adsnasa  isi  scopus
    8. Gerdjikov V.S., Todorov M.D., Kyuldjiev A.V., “Polarization effects in modeling soliton interactions of the Manakov model”, RECENT DEVELOPMENTS IN NONLINEAR ACOUSTICS: 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum (?cully, France, 29 June?3 July 2015), AIP Conference Proceedings, 1684, ed. Todorov M., Amer Inst Physics, 2015, 080006  crossref  isi  scopus
    9. Gerdjikov V.S. Todorov M.D. Kyuldjiev A.V., “Asymptotic Behavior of Manalcov Solitons: Effects of Potential Wells and Humps”, Math. Comput. Simul., 121 (2016), 166–178  crossref  mathscinet  isi  scopus
    10. Gerdjikov V.S., Todorov M.D., Kyuldjiev A.V., “Adiabatic Interactions of Manakov Solitons-Effects of Cross-Modulation”, Wave Motion, 71:SI (2017), 71–81  crossref  mathscinet  isi  scopus
    11. Gerdjikov V.S., Todorov M.D., “Manakov Model With Gain/Loss Terms and N-Soliton Interactions: Effects of Periodic Potentials”, Appl. Numer. Math., 141:SI (2019), 62–80  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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