arXiv subjects

L. A. Cisneros-Ake

Publications and source records attributed to L. A. Cisneros-Ake.

3 recordsLinked to original sources

arXiv2021

Kink-antikink stripe interactions in the two-dimensional sine-Gordon equation

The main focus of the present work is to study quasi-one-dimensional kink-antikink stripes embedded in the two-dimensional sine-Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink stripe on their respective time and space dependent widths and locations. The resulting reduced system of coupled equations is found to accurately describe the width and undulation dynamics of a single kink stripe as well as that of interacting ones. As an aside, we also discuss two related topics: the computational identification of the kink center and its numerical implications and alternative perturbative and multiple scales approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.

nlin.PS↗

arXiv2019

Reduced dynamics for one and two dark soliton stripes in the defocusing nonlinear Schrödinger equation: a variational approach

We study the dynamics and pairwise interactions of dark soliton stripes in the two-dimensional defocusing nonlinear Schrödinger equation. By employing a variational approach we reduce the dynamics for dark soliton stripes to a set of coupled one-dimensional "filament" equations of motion for the position and velocity of the stripe. The method yields good qualitative agreement with the numerical results as regards the transverse instability of the stripes. We propose a phenomenological amendment that also significantly improves the quantitative agreement of the method with the computations. Subsequently, the method is extended for a pair of symmetric dark soliton stripes that include the mutual interactions between the filaments. The reduced equations of motion are compared with a recently proposed adiabatic invariant method and its corresponding findings and are found to provide a more adequate representation of the original full dynamics for a wide range of cases encompassing perturbations with long and short wavelengths, and combinations thereof.

nlin.PS↗

arXiv2019

Dynamics and stabilization of bright soliton stripes in the hyperbolic-dispersion nonlinear Schrödinger equation

We consider the dynamics and stability of bright soliton stripes in the two-dimensional nonlinear Schrödinger equation with hyperbolic dispersion, under the action of transverse perturbations. We start by discussing a recently proposed adiabatic-invariant approximation for transverse instabilities and its limitations in the bright soliton case. We then focus on a variational approximation used to reduce the dynamics of the bright-soliton stripe to effective equations of motion for its transverse shift. The reduction allows us to address the stripe's snaking instability, which is inherently present in the system, and follow the ensuing spatiotemporal undulation dynamics. Further, introducing a channel-shaped potential, we show that the instabilities (not only flexural, but also those of the necking type) can be attenuated, up to the point of complete stabilization of the soliton stripe.

nlin.PS↗