arXiv subjects

Vadym Vekslerchik

Publications and source records attributed to Vadym Vekslerchik.

8 recordsLinked to original sources

arXiv2008

Eigenvalue cut-off in the cubic-quintic nonlinear Schrodinger equation

Using theoretical arguments, we prove the numerically well-known fact that the eigenvalues of all localized stationary solutions of the cubic-quintic 2D+1 nonlinear Schrodinger equation exhibit an upper cut-off value. The existence of the cut-off is inferred using Gagliardo-Nirenberg and Holder inequalities together with Pohozaev identities. We also show that, in the limit of eigenvalues close to zero, the eigenstates of the cubic-quintic nonlinear Schrodinger equation behave similarly to those of the cubic nonlinear Schrodinger equation.

nlin.PS↗

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

Collapse in coupled Nonlinear Schrodinger equations: Sufficient conditions and Applications

In this paper we study blow-up phenomena in general coupled nonlinear Schrodinger equations with different dispersion coefficients. We find sufficient conditions for blow-up and for the existence of global solutions. We discuss several applications of our results to heteronuclear multispecies Bose-Einstein condensates and to degenerate boson-fermion mixtures.

nlin.PS↗

arXiv2006

Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons and discuss other applications of interest to the field of nonlinear matter waves.

nlin.PS↗

arXiv2005

Modulational instability, solitons and periodic waves in models of quantum degenerate Boson-Fermion mixtures

In this paper we study a system of coupled nonlinear Schrodinger equations modelling a quantum degenerate mixture of bosons and fermions. We analyze the stability of plane waves, give precise conditions for the existence of solitons and write explicit solutions in the form of periodic waves. We also check that the solitons observed previously in numerical simulations of the model correspond exactly to our explicit solutions and see how plane waves destabilize to form periodic waves.

nlin.PS↗

arXiv2002

Soliton molecules in trapped vector Nonlinear Schrodinger systems

We study a new class of vector solitons in trapped Nonlinear Schrodinger systems modelling the dynamics of coupled light beams in GRIN Kerr media and atomic mixtures in Bose-Einstein condensates. These solitons exist for different spatial dimensions, their existence is studied by means of a systematic mathematical technique and the analysis is made for inhomogeneous media.

nlin.PS↗

arXiv2001

Exact solutions of the two-mode model of multicomponent Bose-Einstein condensates

We find the explicit solution of a two--mode model used to explain vortex dynamics in multicomponent Bose-Einstein condensates. We prove that all the solutions are constants or periodic functions and give explicit formulae for the time evolution of the populations of the two atomic species present in the condensate.

cond-mat.soft↗

arXiv2001

Construction of exact solutions by spatial traslations in inhomogeneous Nonlinear Schrodinger equations. Applications to Bose-Einstein condensation

In this paper we study a general nonlinear Schrödinger equation with a time dependent harmonic potential. Despite the lack of traslational invariance we find a symmetry trasformation which, up from any solution, produces infinitely many others which are centered on classical trajectories. The results presented here imply that, not only the center of mass of the wave-packet satisfies the Ehrenfest theorem and is decoupled from the dynamics of the wave-packet, but also the shape of the solution is independent of the behaviour of the center of the wave. Our findings have implications on the dynamics of Bose-Einstein condensates in magnetic traps

cond-mat.soft↗