Related papers: Analytical formulation for soliton-potential dynam…
The cooperative dynamics of a 1-D collection of Markov jump, interacting stochastic processes is studied via a mean-field approach. In the time-asymptotic regime, the resulting nonlinear master equation is analytically solved. The…
Interaction of Double sine-Gordon solitons with a space dependent potential wall and also a potential well has been investigated by employing an analytical model based on the collective coordinate approach. The potential has been added to…
A Collective coordinate variable for adding a space dependent potential to the sine-Gordon model is presented. Interaction of solitons with a delta function potential barrier and also delta function potential well is investigated. Most of…
Soliton dynamics in a large variety of longitudinally modulated lattices are studied in terms of phase space analysis for an effective particle approach and direct numerical simulations. Complex soliton dynamics are shown to depend strongly…
We study nonlocal bright solitons subject to external spatially nonuniform potentials. If the potential is slowly varying on the soliton scale, we derive analytical soliton solutions behaving like Newtonian particles. If the potential has…
A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full…
Soliton propagation dynamics under the presence of a complex potential are investigated. A large variety of qualitatively different potentials, including periodic, semi-infinite periodic and localized potentials, is considered. Cases of…
We derive the equations governing the motion of Kerr solitons in pair waveforms. Recent experiments in microresonators have studied a variety of interaction effects in multisoliton waveforms, including collisions and formation of soliton…
We analyse the scattering of a two-dimensional soliton on a potential well. We show that this soliton can pass through the well, bounce back or become trapped and we study the dependence of the critical velocity on the width and the depth…
Dynamics of solitons of the Ablowitz-Ladik model in the presence of a random potential is studied. In absence of the random potential it is an integrable model and the solitons are stable. As a result of the random potential this stability…
An improved model for the soliton-potential interaction is presented. This model is constructed with a better approximation for adding the potential to the lagrangian through a space-time metric. The results of the model are compared with…
Interference patterns associated with soliton-soliton interaction are investigated in detail. We find that the temporal and spatial interference patterns exhibit quite different characteristics. The period of the spatial interference…
An analytical description of polymer melts and their mixtures as liquids of interacting soft colloidal particles is obtained from liquid-state theory. The derived center-of-mass pair correlation functions with no adjustable parameters…
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 obtain analytical expressions for an effective potential of interaction between two- and three-dimensional (2D and 3D) solitons (including the case of 2D vortex solitons) belonging to two different modes which are incoherently coupled by…
An analytical expression for the current through a single level quantum dot for arbitrary strength of the on-site electron-electron interaction is derived beyond standard mean-field theory. By describing the localised states in terms of…
Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three…
We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find…
The nature of the interaction of a soliton with an attractive well is elucidated using a model of two interacting point particles. The system shows the existence of trapped states at positive kinetic energy, as well as reflection by an…
An analytical model for adding a space dependent potential to the phi^4 field is presented, by constructing a collective coordinate for solitary solution of this model. Interaction of the $\phi^{4}$ field with a delta function potential…