arXiv subjects

Gaspar D. Montesinos

Publications and source records attributed to Gaspar D. Montesinos.

8 recordsLinked 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↗

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↗

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

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

Stabilized two-dimensional vector solitons

In this letter we introduce the concept of stabilized vector solitons as nonlinear waves constructed by addition of mutually incoherent Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We analyze the stability of this new kind of structures and describe their behavior and formation in Manakov-like interactions. Potential applications of our results in Bose-Einstein condensation and nonlinear optics are also discussed.

nlin.PS↗

arXiv2003

Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers

We demonstrate that stabilization of solitons of the multidimensional Schrodinger equation with a cubic nonlinearity may be achieved by a suitable periodic control of the nonlinear term. The effect of this control is to stabilize the unstable solitary waves which belong to the frontier between expanding and collapsing solutions and to provide an oscillating solitonic structure, some sort of breather-type solution. We obtain precise conditions on the control parameters to achieve the stabilization and compare our results with accurate numerical simulations of the nonlinear Schrodinger equation. Because of the application of these ideas to matter waves these solutions are some sort of matter breathers.

nlin.PS↗