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TMF, 1999, Volume 118, Number 3, Pages 354–361 (Mi tmf707)  

This article is cited in 8 scientific papers (total in 8 papers)

Structural instability of a soliton for the Davey–Stewartson II equation

R. R. Gadyl'shin, O. M. Kiselev

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

Abstract: An algebraic soliton of the Davey–Stewartson II equation looses structural stability under a small perturbation of the initial data.

DOI: https://doi.org/10.4213/tmf707

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English version:
Theoretical and Mathematical Physics, 1999, 118:3, 278–284

Bibliographic databases:


Citation: R. R. Gadyl'shin, O. M. Kiselev, “Structural instability of a soliton for the Davey–Stewartson II equation”, TMF, 118:3 (1999), 354–361; Theoret. and Math. Phys., 118:3 (1999), 278–284

Citation in format AMSBIB
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\by R.~R.~Gadyl'shin, O.~M.~Kiselev
\paper Structural instability of a soliton for the Davey--Stewartson~II equation
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\yr 1999
\vol 118
\issue 3
\pages 354--361
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\crossref{https://doi.org/10.4213/tmf707}
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\zmath{https://zbmath.org/?q=an:0945.35082}
\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 3
\pages 278--284
\crossref{https://doi.org/10.1007/BF02557322}
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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. 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
    2. 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
    3. 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
    4. Pelinovsky, DE, “A normal form for nonlinear resonance of embedded solitons”, Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 458:2022 (2002), 1469  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. 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
    6. McConnell, M, “Localised coherent solutions of the DSI and DSII equations - a numerical study”, Mathematics and Computers in Simulation, 69:5–6 (2005), 424  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Klein Ch., Saut J.-C., “IST Versus PDE: A Comparative Study”, Hamiltonian Partial Differential Equations and Applications, Fields Institute Communications, eds. Guyenne P., Nicholls D., Sulem C., Springer, 2015, 383–449  crossref  mathscinet  zmath  isi
    8. 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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