Soliton stability in plasmas and hydrodynamics

E. A. Kuznetsov; A. M. Rubenchik; V. E. Zakharov

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

Soliton stability in plasmas and hydrodynamics

E. A. Kuznetsov, A. M. Rubenchik, V. E. Zakharov

Mathematics

Research output: Contribution to journal › Review article › peer-review

491 Scopus citations

Abstract

The stability of solitons is reviewed for nonlinear conservative media. The main attention is paid to the description of the methods: perturbation theory, inverse scattering transform, Lyapunov method. Its applications are demonstrated in detail for the nonlinear Schrödinger equation, the KdV equation, and their generalizations. Applications to problems in plasma physics and hydrodynamics are considered.

Original language	English (US)
Pages (from-to)	103-165
Number of pages	63
Journal	Physics Reports
Volume	142
Issue number	3
DOIs	https://doi.org/10.1016/0370-1573(86)90016-5
State	Published - Sep 1986

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/0370-1573(86)90016-5

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title = "Soliton stability in plasmas and hydrodynamics",

abstract = "The stability of solitons is reviewed for nonlinear conservative media. The main attention is paid to the description of the methods: perturbation theory, inverse scattering transform, Lyapunov method. Its applications are demonstrated in detail for the nonlinear Schr{\"o}dinger equation, the KdV equation, and their generalizations. Applications to problems in plasma physics and hydrodynamics are considered.",

author = "Kuznetsov, {E. A.} and Rubenchik, {A. M.} and Zakharov, {V. E.}",

year = "1986",

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T1 - Soliton stability in plasmas and hydrodynamics

AU - Kuznetsov, E. A.

AU - Rubenchik, A. M.

AU - Zakharov, V. E.

PY - 1986/9

Y1 - 1986/9

N2 - The stability of solitons is reviewed for nonlinear conservative media. The main attention is paid to the description of the methods: perturbation theory, inverse scattering transform, Lyapunov method. Its applications are demonstrated in detail for the nonlinear Schrödinger equation, the KdV equation, and their generalizations. Applications to problems in plasma physics and hydrodynamics are considered.

AB - The stability of solitons is reviewed for nonlinear conservative media. The main attention is paid to the description of the methods: perturbation theory, inverse scattering transform, Lyapunov method. Its applications are demonstrated in detail for the nonlinear Schrödinger equation, the KdV equation, and their generalizations. Applications to problems in plasma physics and hydrodynamics are considered.

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DO - 10.1016/0370-1573(86)90016-5

M3 - Review article

AN - SCOPUS:45949128280

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VL - 142

SP - 103

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JO - Physics Reports

JF - Physics Reports

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ER -

Soliton stability in plasmas and hydrodynamics

Abstract

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