Related papers: Interactions of Parametrically Driven Dark Soliton…
In this manuscript we track the evolution of a system consisting of two self-gravitating virialized objects made of a scalar field in the newtonian limit. The Schr\"odinger-Poisson system contains a potential with self-interaction of the…
We study collisions of moving nonlinear-Schr\"{o}dinger solitons with a $\mathcal{PT}$-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and,…
Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged. The two solitons merge into one…
The effective interactions between two nuclear clusters, $d+d$, $t+t$, and $\alpha+\alpha$, are investigated within a cluster model using local nucleon-nucleon~($NN$) forces. It is shown that the interaction in the spin-aligned $d+d$ system…
We present a numerical study of solutions to the $2d$ cubic and quintic focusing nonlinear Schr\"odinger equation in the exterior of a smooth, compact and strictly convex obstacle (a disk) with Dirichlet boundary condition. We first…
We consider a simple model system supporting stable solitons in two dimensions. The system is the parametrically driven damped nonlinear Schr\"odinger equation, and the soliton stabilises for sufficiently strong damping. The purpose of this…
The well known effect of the linear damping on the moving nonlinear Schr\"odinger soliton (even when there is a supply of energy via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does…
We outline a program to classify domain walls (DWs) and vector solitons in the 1D two-component coupled nonlinear Schrodinger (CNLS) equation with general coefficients. The CNLS equation is reduced first to a complex ordinary differential…
Discrete solitons in the Ablowitz-Ladik (AL) and discrete nonlinear Schr\"odinger (DNLS) equations with damping and strong rapid drive are investigated. The averaged equations have the forms of the parametric AL and DNLS equations. A new…
We consider a generalized nonlinear Schr\"odinger equation (NLS) with a power nonlinearity |\psi|^2\mu\psi, of focusing type, describing propagation on the ramified structure given by N edges connected at a vertex (a star graph). To model…
This work deals with soliton solutions of the nonlinear Schroedinger equation with a diversity of nonlinearities. We solve the equation in a potential which oscillates in time between attractive and expulsive behavior, in the presence of…
Effective pair potentials for hollow nanoparticles like the ones made from carbon (fullerenes) or metal dichalcogenides (inorganic fullerenes) consist of a hard core repulsion and a deep, but short-ranged, van der Waals attraction. We…
In the present work we study discrete nonlinear Schr{\"o}dinger models combining nearest (NN) and next-nearest (NNN) neighbor interactions, motivated by experiments in waveguide arrays. While we consider the more experimentally accessible…
We study the one-dimensional nonlinear Schr\"odinger equation with the cubic-quintic combination of attractive and repulsive nonlinearities, and a trapping potential represented by a delta-function. We determine all bound states with a…
A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial…
In this paper we present some recent results concerning the ex- istence, the stability and the dynamics of solitons occurring in the nonlinear Schroedinger equation when the parameter h -> 0. We focus on the role played by the Energy and…
We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free…
Nonlinear interactions in focusing media between traveling solitons and the dispersive shocks produced by an initial discontinuity are studied using the one-dimensional nonlinear Schrodinger equation. It is shown that, when solitons travel…
The long-time asymptotic behavior of solutions to the focusing nonlinear Schr\"odinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the case of initial conditions that allow for the…
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.…