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Pis'ma v Zh. Èksper. Teoret. Fiz., 2008, Volume 87, Issue 4, Pages 225–229 (Mi jetpl42)  

This article is cited in 5 scientific papers (total in 5 papers)

NONLINEAR DYNAMICS

Bifurcations and the stability of the surface envelope solitons for a finite-depth fluid

D. S. Agafontsev

Landau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russia

Abstract: The dynamics of the quasi-monochromatic surface gravitational waves in a finite-depth fluid is studied for the case where the product of the wavenumber by the depth of the fluid is close to the critical value k cr h ≈ 1.363. Within the framework of the Hamiltonian formalism, the general nonlinear Schrödinger equation is derived. In contrast to the classical nonlinear Schrödinger equation, this equation involves the gradient terms to the four-wave interaction, as well as the six-wave interaction. This equation is used to analyze the modulation instability of the monochromatic waves, as well as the bifurcations of the soliton solutions and their stability. It is shown that the solitons are stable and unstable to finite perturbations for focusing and defocusing nonlinearities, respectively.

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English version:
Journal of Experimental and Theoretical Physics Letters, 2008, 87:4, 195–199

Bibliographic databases:

PACS: 05.45.Yv, 47.20.Ky, 47.55.Dr
Received: 14.01.2008

Citation: D. S. Agafontsev, “Bifurcations and the stability of the surface envelope solitons for a finite-depth fluid”, Pis'ma v Zh. Èksper. Teoret. Fiz., 87:4 (2008), 225–229; JETP Letters, 87:4 (2008), 195–199

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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. JETP Letters, 87:12 (2008), 667–671  mathnet  crossref  isi
    2. E. A. Kuznetsov, D. S. Agafontsev, F. Dias, Zhurn. matem. fiz., anal., geom., 4:4 (2008), 529–550  mathnet  mathscinet  zmath
    3. Kuznetsov E.A., Dias F., Phys Rep, 507:2–3 (2011), 43–105  crossref  mathscinet  adsnasa  isi  elib  scopus
    4. Agafontsev D.S., Zakharov V.E., Phys. Lett. A, 379:40-41 (2015), 2586–2590  crossref  mathscinet  adsnasa  isi  scopus
    5. Tsitoura F., Horikis T.P., Frantzeskakis D.J., Rom. Rep. Phys., 71:2 (2019), 104  isi
  •       Pis'ma v Zhurnal ksperimental'noi i Teoreticheskoi Fiziki
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