Soliton stability in plasmas and hydrodynamics

Кузнецов, Е. А.; Rubenchik, Alexander M.; Захаров, В. Е.

doi:10.1016/0370-1573(86)90016-5

Cited by 528 publications

(372 citation statements)

References 48 publications

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“…Note that this stability indication is consistent with that for the cubic NLS solitons (V.8) which, as is well-known, are stable (see, e.g. [33]). Now we show that the lower soliton branch (µ < 0) is stable: solitons from this branch indeed realize a minimum of the Hamiltonian H for a fixed number of waves N .…”

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confidence: 89%

Deep-water internal solitary waves near critical density ratio

Агафонцев

Dias

Кузнецов

2007

Physica D: Nonlinear Phenomena

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Bifurcations of solitary waves propagating along the interface between two ideal fluids are considered. The study is based on a Hamiltonian approach. It concentrates on values of the density ratio close to a critical one, where the supercritical bifurcation changes to the subcritical one. As the solitary wave velocity approaches the minimum phase velocity of linear interfacial waves (the bifurcation point), the solitary wave solutions transform into envelope solitons. In order to describe their behavior and bifurcations, a generalized nonlinear Schrödinger equation describing the behavior of solitons and their bifurcations is derived. In comparison with the classical NLS equation this equation takes into account three additional nonlinear terms: the so-called Lifshitz term responsible for pulse steepening, a nonlocal term analogous to that first found by Dysthe for gravity waves and the six-wave interaction term. We study both analytically and numerically two solitary wave families of this equation for values of the density ratio ρ that are both above and below the critical density ratio ρcr. For ρ > ρcr, the soliton solution can be found explicitly at the bifurcation point. The maximum amplitude of such a soliton is proportional to √ ρ − ρcr, and at large distances the soliton amplitude decays algebraically. A stability analysis shows that solitons below the critical ratio are stable in the Lyapunov sense in the wide range of soliton parameters. Above the critical density ratio solitons are shown to be unstable with respect to finite perturbations.

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confidence: 89%

Deep-water internal solitary waves near critical density ratio

Агафонцев

Dias

Кузнецов

2007

Physica D: Nonlinear Phenomena

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“…(n, v +c, ϕ)(x −ct, t) and, respectively, (n, v, ϕ)(−x, −t) are solutions, if (n, v, ϕ)(x, t) is a solution. We refer to [15,21,29] and the references therein for more information on the physical background of these equations. A particular solution is found for constant density n ≡ 1, vanishing potential ϕ ≡ 0, and constant velocity v ≡ v 0 ; here v 0 is arbitrary due to Galilean invariance.…”

Section: Introductionmentioning

confidence: 99%

Linear stability and instability of ion-acoustic plasma solitary waves

Hărăguş

Scheel

2002

Physica D: Nonlinear Phenomena

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“…This system of equations, however, is generic and applies to a wide range of physical situations, including nonlinear, nonlocal media for which the response to a beam involves some sort of diffusive mechanism [35], for instance thermo-optic media [36] such as lead glasses [37][38][39] and photorefractive crystals [40]. A similar system of equations also arises in the so-called α models of turbulence [41,42].…”

Section: Introductionmentioning

confidence: 99%