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TMF, 2000, Volume 123, Number 3, Pages 424–432 (Mi tmf613)  

This article is cited in 1 scientific paper (total in 1 paper)

Reduction of the dressing chain of the Schrödinger operator

M. Yu. Kulikova, V. S. Novikovb

a Institute of Applied Physics, Russian Academy of Sciences
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: We reduce the problem of constructing real finite-gap solutions of the focusing modified Korteweg–de Vries equation to the dressing chain of the Schrödinger operator. We show that the Schrödinger operator spectral curve corresponding to such a solution is real. We give some restrictions on the initial data for the chain that lead to such solutions. We also consider a soliton reduction. We obtain compact representations for the multisoliton and breather solutions of the modified Korteweg–de Vries equationentations can be useful in developing the perturbation theory for various applied problems.

DOI: https://doi.org/10.4213/tmf613

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English version:
Theoretical and Mathematical Physics, 2000, 123:3, 768–775

Bibliographic databases:

Received: 16.09.1999

Citation: M. Yu. Kulikov, V. S. Novikov, “Reduction of the dressing chain of the Schrödinger operator”, TMF, 123:3 (2000), 424–432; Theoret. and Math. Phys., 123:3 (2000), 768–775

Citation in format AMSBIB
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\by M.~Yu.~Kulikov, V.~S.~Novikov
\paper Reduction of the dressing chain of the Schr\"odinger operator
\jour TMF
\yr 2000
\vol 123
\issue 3
\pages 424--432
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\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 123
\issue 3
\pages 768--775
\crossref{https://doi.org/10.1007/BF02551031}
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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. Espinosa-Ceron, A, “Soliton dynamics in the complex modified KdV equation with a periodic potential”, Physica D-Nonlinear Phenomena, 236:2 (2007), 141  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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