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Dynamics of Solitons in Nearly Integrable Systems
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…
Chapter 2 - Variational methods in nonlinear fiber optics and related fields
- B. Malomed
Soliton-defect collisions in the nonlinear Schrödinger equation
Abstract We report results of systematic numerical simulations of collisions between a soliton and an attractive defect described by the perturbing term in the nonlinear Schrodinger equation…
Soliton Management in Periodic Systems
- B. Malomed
- 6 July 2006
Periodically modulated dispersion, and dispersion management: basic results for solitons.- The split-step model.- Nonlinearity management for quadratic, cubic, and Bragg-grating solitons.- Resonant…
Stability of solitons in parity-time-symmetric couplers.
Families of analytical solutions are found for symmetric and antisymmetric solitons in a dual-core system with Kerr nonlinearity and parity-time (PT)-balanced gain and loss and a stability region is obtained in an analytical form and verified by simulations.
The variational principle for nonlinear waves in dissipative systems
Abstract We discuss the application of the variational principle to nonlinear dissipative systems, in particular the nonlinear Schrodinger (NLS) equation with diffusive and damping terms. The…
Solitons in nonlinear lattices
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic…
Self-steepening of ultrashort optical pulses without self-phase-modulation
A first optical manifestation of the Chen-Lee-Liu-type derivative nonlinear Schroedinger equation results in self-steepening of ultrashort pulses and shock formation without simultaneous self-phase…
Adiabaticity in nonlinear quantum dynamics: Bose-Einstein condensate in a time-varying box
A simple model of an atomic Bose-Einstein condensate in a box whose size varies with time is studied to determine the nature of adiabaticity in the nonlinear dynamics obtained within the…
Spatiotemporal optical solitons
In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are…