Related papers: Soliton Interactions in Perturbed Nonlinear Schroe…
We study quantum correlations and quantum noise in the soliton collision described by a general two-soliton solution of the nonlinear Schr\"odinger equation, by using the back-propagation method. Our results include the standard case of a…
Dynamics of solitons is considered in the framework of an extended nonlinear Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped…
Small quantum fluctuations in solitons described by the cubic-quintic nonlinear Schr\"{o}dinger equation (CQNLSE) are studied with the linear approximation. The cases of both self-defocusing and self-focusing quintic term are considered (in…
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…
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…
Synchronous collisions of solitons of the Korteweg -- de Vries equation are considered as a representative example of the interaction of a large number of solitons in a soliton gas. Statistical properties of the soliton field are examined…
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…
We demonstrate that periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schr\"{o}dinger (DNLS) equation can strongly facilitate creation of traveling solitons in the lattice. We predict this possibility in an…
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…
A numerical exploration of a gain-loss nonlinear Schr\"odinger equation was carried out utilizing over 180000 core hours to conduct more than 10000 unique simulations in an effort to characterize the model's six dimensional parameter space.…
In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h->0. We prove that under suitable assumptions, the the soliton approximately follows the dynamics of a point particle,…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…
We study systematically the scattering of solitons on localized impurities in the discrete nonlinear Schr\"odinger (DNLS) equation with a saturable nonlinearity. We show that, apart from the generic scenario of the outcome of the scattering…
The dynamics of soliton pulses in the Nonlinear Schrodinger Equation (NLSE) driven by an external Traveling wave is studied analytically and numerically. The Hamiltonian structure of the system is used to show that, in the adiabatic…
We investigate a propagation of solitons for nonlinear Schrodinger equation under small driving force. The driving force passes the resonance. The process of scattering on the resonance leads to changing of number of solitons. After the…
We consider a cubic nonlinear Schroedinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems…
Scalar particles are a common prediction of many beyond the Standard Model theories. If they are light and cold enough, there is a possibility they may form Bose-Einstein condensates, which will then become gravitationally bound. These…
The Boltzmann type kinetic equation for solitons in Nonlinear Schr\"{o}dinger equation has been constructed on the base of analysis of two soliton collision. Possible applications for Langmuir solitons in plasma and solitons in optic fiber…
We analyze a system of three two-dimensional nonlinear Schr\"odinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time…