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Teoreticheskaya i Matematicheskaya Fizika, 1983, Volume 56, Number 1, Pages 131–136 (Mi tmf2197)  

This article is cited in 33 scientific papers (total in 33 papers)

On the integrability of equations of Davey–Stewartson type

E. I. Shulman
References:
Abstract: Equations of Davey–Stewartson type for nondegenerate dispersion taw are considered. It is shown that in two spatial dimensions all cases of their integrability reduce to ones already known, while in three spatial dimensions these equations are nonintegrable.
Received: 22.07.1982
English version:
Theoretical and Mathematical Physics, 1983, Volume 56, Issue 1, Pages 720–724
DOI: https://doi.org/10.1007/BF01027548
Bibliographic databases:
Language: Russian
Citation: E. I. Shulman, “On the integrability of equations of Davey–Stewartson type”, TMF, 56:1 (1983), 131–136; Theoret. and Math. Phys., 56:1 (1983), 720–724
Citation in format AMSBIB
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\paper On the integrability of equations of Davey--Stewartson type
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\pages 131--136
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\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 56
\issue 1
\pages 720--724
\crossref{https://doi.org/10.1007/BF01027548}
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Linking options:
  • https://www.mathnet.ru/eng/tmf2197
  • https://www.mathnet.ru/eng/tmf/v56/i1/p131
  • This publication is cited in the following 33 articles:
    1. Sheng-Nan Wang, Han-Han Sheng, Guo-Fu Yu, “Dynamics of the coupled (2+1)-dimensional Fokas system”, Z. Angew. Math. Phys., 76:1 (2025)  crossref
    2. Yulei Cao, Jingsong He, Yi Cheng, “New localized wave structures in the Maccari system”, Nonlinear Dyn, 2024  crossref
    3. Yu Zhao, Bo Tian, Cong-Cong Hu, Su-Su Chen, Shao-Hua Liu, “Interactions among the Rogue Waves and Solitons for a (2+1)-dimensional Maccari System in Fluid Mechanics and Nonlinear Optics”, Qual. Theory Dyn. Syst., 22:4 (2023)  crossref
    4. Yu-Lan Ma, Abdul-Majid Wazwaz, Bang-Qing Li, “Soliton resonances, soliton molecules, soliton oscillations and heterotypic solitons for the nonlinear Maccari system”, Nonlinear Dyn, 111:19 (2023), 18331  crossref
    5. Asymptotic Perturbation Methods, 2023, 219  crossref
    6. Fu H., Ruan Ch., Hu W., “Soliton Solutions to the Nonlocal Davey-Stewartson III Equation”, Mod. Phys. Lett. B, 35:1 (2021), 2150026  crossref  isi
    7. Yulei Cao, Yi Cheng, Boris A. Malomed, Jingsong He, “Rogue waves and lumps on the nonzero background in the ‐symmetric nonlocal Maccari system”, Stud Appl Math, 147:2 (2021), 694  crossref
    8. Asma Issasfa, Ji Lin, “N-soliton and rogue wave solutions of (2+1)-dimensional integrable system with Lax pair”, Int. J. Mod. Phys. B, 33:27 (2019), 1950317  crossref
    9. Jiguang Rao, Dumitru Mihalache, Yi Cheng, Jingsong He, “Lump-soliton solutions to the Fokas system”, Physics Letters A, 383:11 (2019), 1138  crossref
    10. Jiguang Rao, Kuppuswamy Porsezian, Jingsong He, “Semi-rational solutions of the third-type Davey-Stewartson equation”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 27:8 (2017)  crossref
    11. Javier Villarroel, Julia Prada, Pilar G Estévez, “Weakly decaying solutions of nonlinear Schrödinger equation in the plane”, J. Phys. A: Math. Theor., 50:49 (2017), 495203  crossref
    12. Javier Villarroel, Julia Prada, Pilar G. Estévez, “Discrete Spectrum of 2 + 1-Dimensional Nonlinear Schrödinger Equation and Dynamics of Lumps”, Advances in Mathematical Physics, 2016 (2016), 1  crossref
    13. Klein Ch., Saut J.-C., “a Numerical Approach To Blow-Up Issues For Davey-Stewartson II Systems”, Commun. Pure Appl. Anal, 14:4 (2015), 1443–1467  crossref  isi
    14. 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
    15. Javier Villarroel, Julia Prada, “Considerations on conserved quantities and boundary conditions of the 2+1-dimensional nonlinear Schrödinger equation”, Physica D: Nonlinear Phenomena, 300 (2015), 15  crossref
    16. A. Eden, T.B. Gürel, “On the integrability of a generalized Davey–Stewartson system”, Physica D: Nonlinear Phenomena, 259 (2013), 1  crossref
    17. Yong Liang, Mohammad-Reza Alam, “Finite-depth capillary-gravity dromions”, Phys. Rev. E, 88:3 (2013)  crossref
    18. P G Estévez, J Prada, J Villarroel, “On an algorithmic construction of lump solutions in a 2+1 integrable equation”, J. Phys. A: Math. Theor., 40:26 (2007), 7213  crossref
    19. C. Rogers, W. K. Schief, Bäcklund and Darboux Transformations, 2002  crossref
    20. A. Degasperis, C. Rogers, W. K. Schief, “Isothermic Surfaces Generated via Bäcklund and Moutard Transformations: Boomeron and Zoomeron Connections”, Stud Appl Math, 109:1 (2002), 39  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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