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Register a new userMulticomponent long-wave--short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons
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We consider a general multicomponent (2+1)-dimensional long-wave--short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long-wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painleve analysis. Then we construct the exact bright multi-soliton solutions by applying the Hirotas bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.
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A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton trains in the quasi one-dimensional confinement is shown. Additionally, fragmentation of a BEC has been observed outside confinement, in free space. In the end a double BEC production setup for studying soliton collisions is described.
We show how access to sufficiently flexible trapping potentials could be exploited in the generation of three-dimensional atomic bright matter-wave solitons. Our proposal provides a route towards producing bright solitonic states with good fidelity, in contrast to, for example, a non-adiabatic sweeping of an applied magnetic field through a Feshbach resonance.
We employ the generic three-wave system, with the $chi ^{(2)}$ interaction between two components of the fundamental-frequency (FF) wave and second-harmonic (SH) one, to consider collisions of truncated Airy waves (TAWs) and three-wave solitons in a setting which is not available in other nonlinear systems. The advantage is that the single-wave TAWs, carried by either one of the FF component, are not distorted by the nonlinearity and are stable, three-wave solitons being stable too in the same system. The collision between mutually symmetric TAWs, carried by the different FF components, transforms them into a set of solitons, the number of which decreases with the increase of the total power. The TAW absorbs an incident small-power soliton, and a high-power soliton absorbs the TAW. Between these limits, the collision with an incident soliton converts the TAW into two solitons, with a remnant of the TAW attached to one of them, or leads to formation of a complex TAW-soliton bound state. At large velocities, the collisions become quasi-elastic.
Formation of bright envelope solitons from wave packets with a repulsive nonlinearity was observed for the first time. The experiments used surface spin-wave packets in magnetic yttrium iron garnet (YIG) thin film strips. When the wave packets are narrow and have low power, they undergo self-broadening during the propagation. When the wave packets are relatively wide or their power is relatively high, they can experience self-narrowing or even evolve into bright solitons. The experimental results were reproduced by numerical simulations based on a modified nonlinear Schrodinger equation model.
A Lagrangian based method is used to derive an analytical model for studying the dynamics of matter-wave bright soliton created in a harmonic potential which is attractive in the transverse direction and expulsive in the longitudinal direction. By means of sech trial functions and a Ritz optimization procedure, evolution eqautions are constructed for width, amplitude and nonlinear frequency chirp of the propagating soliton of the atomic condensate. Our eqaution for the width is an exact agreement with that of Carr and Castin $[ Phys. Rev. A {bf{66}}, 063602 (2002)]$, obtained by more detailed analysis. In agreement with the experiment of Paris group $[ Science {bf{296}}, 1290 (2002)]$, the expulsive potential is found to cause the soliton to explode for $N|a_s|=0.98$, $N$ being the number of atoms in the condensate and $a_s$, the scattering length of the atom-atom interaction.
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