Related papers: Interactions of solitons with an external force fi…
We investigate the interaction of solitons with an external periodic field within the framework of the modified Korteweg-de Vries (mKdV) equation. In the case of small perturbation a simple dynamical system is used to describe the soliton…
Algebraic soliton interactions with a periodic or quasi-periodic random force are investigated using the Benjamin-Ono equation. The random force is modeled as a Fourier series with a finite number of modes and random phases uniformly…
The aim of this work is to study asymptotically and numerically the interaction of solitons with an external forcing with variable speed using the forced modified Korteweg-de Vries equation (mKdV). We show that the asymptotic predictions…
We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the…
We study the collision of two fast solitons for the nonlinear Schr\"odinger equation in the presence of a spatially adiabatic external potential. For a high initial relative speed $\|v\|$ of the solitons, we show that, up to times of order…
The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation.…
In this Letter we further develop the proposed approach of optical manipulation based on the interactions of non-linear optical effects with nanoparticles. The interaction of the dissipative optical solitons with nanoparticles is studied…
We present the explicit dark-bright three soliton solution and the associated spectral problem for the variable coefficient integrable coupled NLS equation. Using asymptotic analysis as well as graphical analysis we study the interactions…
We use soliton perturbation theory and collective coordinate ansatz to investigate the mechanism of soliton ratchets in a driven and damped asymmetric double sine-Gordon equation. We show that, at the second order of the perturbation…
Interactions between solitons and the coherent oscillation structures generated by localized disturbances via modulational instability are studied within the framework of the focusing nonlinear Schrodinger equation. Two main interaction…
Employing a particularly suitable higher order symplectic integration algorithm, we integrate the 1-$d$ nonlinear Schr\"odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an…
The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced…
We investigate the dynamics of solitons in generalized Klein-Gordon equations in the presence of nonlinear damping and spatiotemporal perturbations. We will present different mechanisms for soliton explosions. We show (both analytically and…
We revise the solutions of the forced Korteweg-de Vries equation describing a resonant interaction of a solitary wave with external pulse-type perturbations. In contrast to previous works where only the limiting cases of a very narrow…
The mechanism underlying the soliton ratchet, both in absence and in presence of noise, is investigated. We show the existence of an asymmetric internal mode on the soliton profile which couples, trough the damping in the system, to the…
We address the interactions between optical solitons in the system with longitudinally varying nonlocality degree and nonlinearity strength. We consider a physical model describing light propagation in nematic liquid crystals featuring a…
We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent…
We present numerical studies of the transport dynamics of a charged soliton in conjugated polymers under the influence of an external time-dependent electric field. All relevant electron-phonon and electron-electron interactions are nearly…
In this paper we study dynamics of solitons in the generalized nonlinear Schr\"odinger equation (NLS) with an external potential in all dimensions except for 2. For a certain class of nonlinearities such an equation has solutions which are…
The problem of soliton-soliton force is revisited. From the exact two solitons solution of a nonautonomous Gross-Pitaevskii equation, we derive a generalized formula for the mutual force between two solitons. The force is given for…