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TMF, 1996, Volume 106, Number 2, Pages 200–208 (Mi tmf1107)  

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

On nonsolution structure of scattering data under perturbation of two-dimensional soliton for Davey–Stewartson equation II

R. R. Gadyl'shin, O. M. Kiselev

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: Asymptotics of the scattering data is constructed for Davey–Stewartson II equation in the case of perturbation of soliton. It is shown that the scattering data of the perturbed problem have a nonsoliton structure.

DOI: https://doi.org/10.4213/tmf1107

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English version:
Theoretical and Mathematical Physics, 1996, 106:2, 167–173

Bibliographic databases:

Received: 31.03.1995

Citation: R. R. Gadyl'shin, O. M. Kiselev, “On nonsolution structure of scattering data under perturbation of two-dimensional soliton for Davey–Stewartson equation II”, TMF, 106:2 (1996), 200–208; Theoret. and Math. Phys., 106:2 (1996), 167–173

Citation in format AMSBIB
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\by R.~R.~Gadyl'shin, O.~M.~Kiselev
\paper On nonsolution structure of scattering data under perturbation of two-dimensional soliton for Davey--Stewartson equation~II
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\transl
\jour Theoret. and Math. Phys.
\yr 1996
\vol 106
\issue 2
\pages 167--173
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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. Kiselev, OM, “Perturbation theory for the Dirac equation in two-dimensional space”, Journal of Mathematical Physics, 39:4 (1998), 2333  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. R. R. Gadyl'shin, O. M. Kiselev, “Structural instability of a soliton for the Davey–Stewartson II equation”, Theoret. and Math. Phys., 118:3 (1999), 278–284  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Kiselev, OM, “Dromion perturbation for the Davey-Stewartson-1 equations”, Journal of Nonlinear Mathematical Physics, 7:4 (2000), 411  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. Pelinovsky, DE, “Spectral decomposition for the Dirac system associated to the DSII equation”, Inverse Problems, 16:1 (2000), 59  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. Fokas, AS, “Interaction of lumps with a line soliton for the DSII equation”, Physica D-Nonlinear Phenomena, 152 (2001), 189  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. Pelinovsky, D, “Gauge transformation and spectral decomposition for the Ishimori-II equations”, Journal of Physics A-Mathematical and General, 36:20 (2003), 5557  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230  mathnet  crossref  mathscinet  zmath  elib
    8. Glebov, S, “Slow passage through resonance for a weakly nonlinear dispersive wave”, SIAM Journal on Applied Mathematics, 65:6 (2005), 2158  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Yurova A.A., Yurov V.A., “Evolyutsiya pervonachalno lokalizovannogo impulsa v uravnenii devi-styuartsona ii tipa”, Izvestiya Kaliningradskogo gosudarstvennogo tekhnicheskogo universiteta, 2011, no. 20, 84–88  elib
    10. Yurova A.A., “Dinamika lokalizovannogo impulsa, opisyvaemogo uravneniem devi - styuartsona ii”, Vestnik Baltiiskogo federalnogo universiteta im. I. Kanta, 2011, no. 5, 12–17  elib
    11. Brown R.M. Perry P.A., “Soliton Solutions and Their (in)Stability For the Focusing Davey-Stewartson II Equation”, Nonlinearity, 31:9 (2018), 4290–4325  crossref  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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