Showing papers by "Yuri S. Kivshar published in 1989"

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.

Dynamics of coupled dark and bright optical solitons.

Abstract: We theoretically examine the interaction between two solitons in a double-mode optical fiber. The bound state between two solitons of different modes is investigated, including both dark and bright solitons. It is shown that interaction between dark solitons as well as between bright solitons is always attractive, but the interaction between bright and dark solitons may be repulsive. Analytical results are in agreement with numerical ones.

Interaction of solitons in tunnel-coupled optical fibers.

Abstract: A pair of weakly interacting optical fibers, which are described by two nonlinear Schrodinger equations with linear coupling terms, is considered in the framework of perturbation theory. It is shown that the interaction of optical solitons in this system is inelastic and that they may form a bound state (bisoliton). The stability and internal oscillations of the bisoliton are also investigated.

Dark-soliton generation in optical fibers

Abstract: We study the generation of dark-pulse solitons in nonlinear-optical fibers in the normal dispersion regime. We demonstrate that dark solitons may be created as pairs by an arbitrary dark pulse without a threshold and obtain the parameters of the generated solitons. The cases of soliton creation by a boxlike dark pulse and a random Gaussian pulse are also described.

Interaction of a fluxon with an inductance step in a long Josephson junction

Abstract: Within the framework of the sine‐Gordon model of a long Josephson junction, we have calculated a threshold value of bias current density which admits capture of a fluxon by an effective potential well generated by a step of inductance in the junction. Along with a kinematic approximation, a nontrivial dynamical correction is found. We have also calculated analytically energy emitted by a fast fluxon moving past the step.