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Dynamics of solitons in nearly integrable systems

Yuri S. Kivshar and Boris A. Malomed

Yuri S. Kivshar

  • Institute for Low Temperature Physics and Engineering of the Academy of Sciences of the Ukraine, Kharkov 310164, Union of Soviet Socialist Republics

Boris A. Malomed

  • P. P. Shirshov Institute for Oceanology of the U.S.S.R. Academy of Sciences, Moscow 117218, Union of Soviet Socialist Republics

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Rev. Mod. Phys. 61, 763 – Published 1 October, 1989

DOI: https://doi.org/10.1103/RevModPhys.61.763

Abstract

A detailed survey of the technique of perturbation theory for nearly integrable systems, based upon the inverse scattering transform, and a minute account of results obtained by means of that technique and alternative methods are given. Attention is focused on four classical nonlinear equations: the Korteweg-de Vries, nonlinear Schrödinger, sine-Gordon, and Landau-Lifshitz equations perturbed by various Hamiltonian and/or dissipative terms; a comprehensive list of physical applications of these perturbed equations is compiled. Systems of weakly coupled equations, which become exactly integrable when decoupled, are also considered in detail. Adiabatic and radiative effects in dynamics of one and several solitons (both simple and compound) are analyzed. Generalizations of the perturbation theory to quasi-one-dimensional and quantum (semiclassical) solitons, as well as to nonsoliton nonlinear wave packets, are also considered.

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See Also

Addendum: Dynamics of solitons in nearly integrable systems

Yuri S. Kivshar and Boris A. Malomed
Rev. Mod. Phys. 63, 211 (1991)

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Rev. Mod. Phys. 61, 763– Published 1 October, 1989

    © 1989 American Physical Society

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