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Dynamics of solitons in nearly integrable systems
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 Schr\"odinger, 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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Citations
Cited by
Pattern formation outside of equilibrium
Cross, M. C., & Hohenberg, P. C. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.851 · Cited by 7,859
Dynamics of Bose-Einstein condensates: Variational solutions of the Gross-Pitaevskii equations
Pérez-García, V. M., Michinel, H., Cirac, J. I., Lewenstein, M., & Zoller, P. (1997) · Physical Review A · doi:10.1103/physreva.56.1424 · Cited by 406
Metadata
- Authors
- Kivshar, Y. S., & Malomed, B. A.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1989-10-01
- Volume
- 61
- Issue
- 4
- Pages
- 763-915
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W2115600080
- Cited by
- 1,854
- References
- 0
- FWCI
- 36.32
- Type
- journal article
- Language
- en
- Open access
- closed
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- Kivshar, Y. S., & Malomed, B. A. (1989). Dynamics of solitons in nearly integrable systems. Reviews of Modern Physics. https://doi.org/10.1103/revmodphys.61.763
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