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Vladimir V. Konotop

Publications and source records attributed to Vladimir V. Konotop.

120 records · Page 7Linked to original sources
arXiv2008

Localized nonlinear waves in systems with time- and space-modulated nonlinearities

Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schrödinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly non-trivial solutions such as periodic (breathers), resonant or quasiperiodically oscillating solitons. Some implications to the field of matter-waves are also discussed.

nlin.PS↗
arXiv2008

Stability of excited states of a Bose-Einstein condensate in an anharmonic trap

We analyze the stability of non-ground nonlinear states of a Bose-Einstein condensate in the mean field limit in effectively 1D (``cigar-shape'') traps for various types of confining potentials. We find that nonlinear states become, in general, more stable when switching from a harmonic potential to an anharmonic one. We discuss the relation between this fact and the specifics of the harmonic potential which has an equidistant spectrum.

nlin.PS↗
arXiv2008

Localized and periodic exact solutions to the nonlinear Schrodinger equation with spatially modulated parameters: Linear and nonlinear lattices

Using similarity transformations we construct explicit solutions of the nonlinear Schrodinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.

nlin.PS↗
arXiv2008

Collapse in boson-fermion mixtures with all-repulsive interactions

We describe the collapse of the bosonic component in a boson-fermion mixture due to the pressure exerted on them by a large fermionic component, leading to collapse in a system with all-repulsive interactions. We describe the phenomena early collapse and of super-slow collapse of the mixture.

nlin.PS↗
arXiv2005

Similarity transformations for Nonlinear Schrodinger Equations with time varying coefficients: Exact results

In this paper we use a similarity transformation connecting some families of Nonlinear Schrodinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrodinger equation. This transformation allows one to apply all known results for that equation to the non-autonomous case with the additional dynamics introduced by the transformation itself. In particular, using stationary solutions of the autonomous nonlinear Schrodinger equation we can construct exact breathing solutions to multidimensional non-autonomous nonlinear Schrodinger equations. An application is given in which we explicitly construct time dependent coefficients leading to solutions displaying weak collapse in three-dimensional scenarios. Our results can find physical applicability in mean field models of Bose-Einstein condensates and in the field of dispersion-managed optical systems.

nlin.PS↗
arXiv2004

Landau dynamics of a grey soliton in a trapped condensate

It is shown that grey soliton dynamics in an one-dimensional trap can be treated as Landau dynamics of a quasi-particle. A soliton of arbitrary amplitude moves in the trapping potential without deformation of its density profile as a particle of mass $2m$. The dynamics in the local density approximation is shown to be consistent with the perturbation theory for dark solitons. Dynamics of a vortex ring in a trap is discussed qualitatively.

cond-mat.stat-mech↗
arXiv2003

Feshbach resonance induced shock waves in Bose-Einstein condensates

We propose a method for generating shock waves in Bose-Einstein condensates by rapidly increasing the value of the nonlinear coefficient using Feshbach resonances. We show that in a cigar-shaped condensate there exist primary (transverse) and secondary (longitudinal) shock waves. We analyze how the shocks are generated in multidimensional scenarios and describe the phenomenology associated with the phenomenon.

cond-mat.soft↗
arXiv2001

Nonlinear Modulation of Multi-Dimensional Lattice Waves

The equations governing weakly nonlinear modulations of $N$-dimensional lattices are considered using a quasi-discrete multiple-scale approach. It is found that the evolution of a short wave packet for a lattice system with cubic and quartic interatomic potentials is governed by generalized Davey-Stewartson (GDS) equations, which include mean motion induced by the oscillatory wave packet through cubic interatomic interaction. The GDS equations derived here are more general than those known in the theory of water waves because of the anisotropy inherent in lattices. Generalized Kadomtsev-Petviashvili equations describing the evolution of long wavelength acoustic modes in two and three dimensional lattices are also presented. Then the modulational instability of a $N$-dimensional Stokes lattice wave is discussed based on the $N$-dimensional GDS equations obtained. Finally, the one- and two-soliton solutions of two-dimensional GDS equations are provided by means of Hirota's bilinear transformation method.

cond-mat.stat-mech↗
arXiv2001

On the applicability of the classical dipole-dipole interaction for polar Bose-Einstein condensates

We argue that the classical form of the dipole-dipole interaction energy cannot be used to model the interaction of the bosons in a dilute Bose-Einstein condensate made of polar atoms. This fact is due to convergence of integrals, if no additional restrictions are introduced. The problem can be regularized, in particular, by introducing a hard sphere model. As an example we propose a regularization consistent with the long range behavior of the effective potential and with the scattering amplitude of the fast particles.

cond-mat.soft↗
arXiv2000

Solutions of Gross-Pitaevskii equations beyond the hydrodynamic approximation: Application to the vortex problem

We develop the multiscale technique to describe excitations of a Bose-Einstein condensate (BEC) whose characteristic scales are comparable with the healing length, thus going beyond the conventional hydrodynamical approximation. As an application of the theory we derive approximate explicit vortex and other solutions. The dynamical stability of the vortex is discussed on the basis of the mathematical framework developed here, the result being that its stability is granted at least up to times of the order of seconds, which is the condensate lifetime. Our analytical results are confirmed by the numerical simulations.

cond-mat.stat-mech↗
arXiv1999

"Quadratic solitons" in nonlinear dynamiical latticess

We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly coupled two-component dipoles in an anisotropic nonlinear host medium. Unlike this discrete system, its continuum counterpart gives rise to the matching conditions only in a trivial degenerate situation. A system of nonlinear evolution equations for slowly varying envelope functions of the resonantly coupled fundamental- and second-harmonic waves is derived. In the one-dimensional case, it coincides with the standard system known in nonlinear optics, which gives rise to stable solitons. In the multidimensional case, the system prove to be more general than its counterpart in optics, because of the anisotropy of the underlying lattice model.

cond-mat.stat-mech↗