Related papers: Colliding solitons for the nonlinear Schrodinger e…
We introduce a model based on a system of coupled nonlinear Schrodinger (NLS) equations with opposite signs infront of the kinetic and gradient terms in the two equations. It also includes time-dependent nonlinearity coefficients and a…
In this paper, we discus the fascinating energy sharing collisions of multicomponent solitons in certain incoherently coupled and coherently coupled nonlinear Schr\"odinger type equations arising in the context of nonlinear optics.
A method for approximating dark soliton solutions of the nonlinear Schrodinger equation under the influence of perturbations is presented. The problem is broken into an inner region, where core of the soliton resides, and an outer region,…
Electrons colliding with spatially fixed ions in strong laser fields are investigated by solving the time-dependent Schr\"odinger equation. Considering first simple one-dimensional model systems, the mechanisms and energy spectra of fast…
We derive a closed expression for the spatial shift experienced by a black soliton colliding with a shallow dark soliton in the context of deformed non-linear Schr\"{o}dinger models. A perturbative scheme is developed based on the expansion…
The interaction of two rectangular pulses in nonlinear Schroedinger model is studied by solving the appropriate Zakharov-Shabat system. It is shown that two real pulses may result in appearance of moving solitons. Different limiting cases,…
We study the dynamics of solitons under the action of one-dimensional quasiperiodic lattice potentials, fractional diffraction, and nonlinearity. The formation and stability of the solitons is investigated in the framework of the fractional…
We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schroedinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and periodic potentials. Parameter regions are presented for broken…
The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by…
The stability and collapse of fundamental unstaggered bright solitons in the discrete Schrodinger equation with the nonpolynomial on-site nonlinearity, which models a nearly one-dimensional Bose-Einstein condensate trapped in a deep optical…
We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of…
We investigate the dynamics of travelling oscillating solitons of the cubic NLS equation under an external spatiotemporal forcing of the form $f(x,t) = a \exp[iK(t)x]$. For the case of time-independent forcing a stability criterion for…
We consider the statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic…
We study solitons in the two-dimensional defocusing nonlinear Schroedinger equation with the spatio-temporal modulation of the external potential. The spatial modulation is due to a square lattice; the resulting macroscopic diffraction is…
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,…
In this paper we study the long time behavior of a discrete approximation in time and space of the cubic nonlinear Schr\"odinger equation on the real line. More precisely, we consider a symplectic time splitting integrator applied to a…
We study the dynamics of emission of radiation (small-amplitude waves) in fast collisions between two solitons of the nonlinear Schr\"odinger (NLS) equation in the presence of weak cubic loss. We calculate the radiation dynamics by a…
Scattering of solitons and dark solitons by potential walls is studied in the nonlinear Schroedinger equation under various conditions. We investigate the conditions under which solitons are split into two solitons at the potential wall. We…
This paper is concerned with the interaction of two solitons of nearly equal speeds for the (BBM) equation. This work is an extension of the results obtained in arXiv:0910.3204 by the same authors, addressing the same question for the…
Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation from a moving small-amplitude soliton in the discrete nonlinear Schr\"odinger equation. When the nonlinearity is of the cubic type, this amplitude is…