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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2008, Volume 87, Issue 4, Pages 225–229
(Mi jetpl42)
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This article is cited in 6 scientific papers (total in 6 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.
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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https://www.mathnet.ru/eng/jetpl42 https://www.mathnet.ru/eng/jetpl/v87/i4/p225
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Abstract page: | 575 | Full-text PDF : | 126 | References: | 34 |
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