arXiv subjects

Victor M. Perez-Garcia

Publications and source records attributed to Victor M. Perez-Garcia.

At least 37 records · Page 2Linked to original sources

arXiv2007

Stabilization of high-order solutions of the cubic Nonlinear Schrodinger Equation

In this paper we consider the stabilization of non-fundamental unstable stationary solutions of the cubic nonlinear Schrodinger equation. Specifically we study the stabilization of radially symmetric solutions with nodes and asymmetric complex stationary solutions. For the first ones we find partial stabilization similar to that recently found for vortex solutions while for the later ones stabilization does not seem possible.

nlin.PS↗

arXiv2007

Nonlinear Supression of Tunneling and Strong Localization in Bose-Einstein Condensates with Spatially Inhomogeneous Interactions

We study the properties of the ground state of Bose-Einstein condensates with spatially inhomogeneous interactions and show that the atom density experiences a strong localization at the spatial region where the scattering length is close to zero while tunneling to regions with positive values of the scattering length is strongly supressed by the nonlinear interactions.

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↗

arXiv2006

Dissipative solitons which cannot be trapped

In this paper we study the behavior of dissipative solitons in systems with high order nonlinear dissipation and show how they cannot survive under the effect of trapping potentials both of rigid wall type or asymptotically increasing ones. This provides an striking example of a soliton which cannot be trapped and only survives to the action of a weak potential.

nlin.PS↗

arXiv2006

Levitation of Bose-Einstein condensates induced by macroscopic non-adiabatic quantum tunneling

We study the dynamics of two-component Bose-Einstein condensates trapped in different vertical positions in the presence of an oscillating magnetic field. It is shown here how tuning appropriately the oscillation frequency of the magnetic field leads to the levitation of the system against gravity. This phenomenon is a manifestation of a macroscopic non-adiabatic tunneling in a system with internal degrees of freedom.

cond-mat.other↗

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↗

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↗

arXiv2005

Matter-wave solitons supported by dissipation

We show how novel types of long-lived self-localized matter waves can be constructed with Bose-Einstein condensates. The ingredients leading to such structures are a spatial phase generating a flux of atoms towards the condensate center and the dissipative mechanism provided by the inelastic three-body collisions in atomic Bose-Einstein condensates. The outcome is an striking example of nonlinear structure supported by dissipation.

nlin.PS↗

arXiv2005

The method of moments for Nonlinear Schrodinger Equations: Theory and Applications

The method of moments in the context of Nonlinear Schrodinger Equations relies on defining a set of integral quantities, which characterize the solution of this partial differential equation and whose evolution can be obtained from a set of ordinary differential equations. In this paper we find all cases in which the method of moments leads to closed evolution equations, thus extending and unifying previous works in the field of applications. For some cases in which the method fails to provide rigorous information we also develop approximate methods based on it, which allow to get some approximate information on the dynamics of the solutions of the Nonlinear Schrodinger equation.

nlin.PS↗

arXiv2005

Turning light into a liquid via atomic coherence

We study a four level atomic system with electromagnetically induced transparency with giant $χ^{(3)}$ and $χ^{(5)}$ susceptibilities of opposite signs. This system would allow to obtain multidimensional solitons and light condensates with surface tension properties analogous to those of usual liquids.

nlin.PS↗

arXiv2005

Symbiotic Solitons in Heteronuclear Multicomponent Bose-Einstein condensates

We show that bright solitons exist in quasi-one dimensional heteronuclear multicomponent Bose-Einstein condensates with repulsive self-interaction and attractive inter-species interaction. They are remarkably robust to perturbations of initial data and collisions and can be generated by the mechanism of modulational instability. Some possibilities for control and the behavior of the system in three dimensions are also discussed.

cond-mat.other↗

arXiv2004

n-body dynamics of stabilized vector solitons

In this work we study the interactions between stabilized Townes solitons. By means of effective Lagrangian methods, we have found that the interactions between these solitons are governed by central forces, in a first approximation. In our numerical simulations we describe different types of orbits, deflections, trapping and soliton splitting. Splitting phenomena are also described by finite dimensional reduced models. All these effects could be used for potential applications of stabilized solitons.

nlin.PS↗

arXiv2004

Stable propagation of pulsed beams in Kerr focusing media with modulated dispersion

We propose the modulation of dispersion to prevent collapse of planar pulsed beams which propagate in Kerr-type self-focusing optical media. As a result, we find a new type of two-dimensional spatio-temporal solitons stabilized by dispersion management. We have studied the existence and properties of these solitary waves both analytically and numerically. We show that the adequate choice of the modulation parameters optimizes the stabilization of the pulse.

nlin.PS↗

arXiv2004

Spectral Methods for Partial Differential Equations in Irregular Domains: The Spectral Smoothed Boundary Method

In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its capability to deal with domains of arbitrary shape and its easy implementation via Fast Fourier Transform routines. We discuss several examples of practical interest and test the results against exact solutions and standard numerical methods.

math.NA↗

arXiv2004

Stabilized vortex solitons in layered Kerr media

In this letter we demonstrate the possibility of stabilizing beams with angular momentum propagating in Kerr media. Large propagation distances without filamentation can be achieved in layered media with alternating focusing and defocusing nonlinearities. Stronger stabilization can be obtained with the addition of an incoherent beam.

nlin.PS↗

arXiv2003

Numerical studies of stabilized Townes solitons

We study numerically stabilized solutions of the two-dimensional Schrodinger equation with a cubic nonlinearity. We discuss in detail the numerical scheme used and explain why choosing the right numerical strategy is very important to avoid misleading results. We show that stabilized solutions are Townes solitons, a fact which had only been conjectured previously. Also we make a systematic study of the parameter regions in which these structures exist.

nlin.PS↗

arXiv2003

Self-similar solutions and collective coordinate methods for Nonlinear Schrodinger Equations

In this paper we study the phase of self-similar solutions to general Nonlinear Schrödinger equations. From this analysis we gain insight on the dynamics of nontrivial solutions and a deeper understanding of the way collective coordinate methods work. We also find general evolution equations for the most relevant dynamical parameter $w(t)$ corresponding to the width of the solution. These equations are exact for self-similar solutions and provide a shortcut to find approximate evolution equations for the width of non-self-similar solutions similar to those of collective coordinate methods.

nlin.PS↗

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↗