77 citations · 492 across the 25 of their papers we have counts for
25 papers
Kinks of fractional models: existence, uniqueness, monotonicity, stability, and sharp asymptotics
Atanas G. Stefanov, P. G. Kevrekidis
In the present work we construct kink solutions for different (parabolic and wave) variants of the fractional model, in both the sub-Laplacian and super-Laplacian setting. We…
Dynamical Instability of 3d Stationary and Traveling Planar Dark Solitons
T. Mithun, A. R. Fritsch, I. B. Spielman +1
Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional Bose-Einstein condensates by quantitatively comparing theoretical…
Revisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach
Ross Parker, Jesús Cuevas-Maraver, P. G. Kevrekidis +1
We consider the existence and spectral stability of multi-breather structures in the discrete Klein-Gordon equation, both for soft and hard symmetric potentials. To obtain analytic…
Kink-antikink stripe interactions in the two-dimensional sine-Gordon equation
R. Carretero-Gonzalez, L. A. Cisneros-Ake, R. Decker +4
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 re…
Stationary multi-kinks in the discrete sine-Gordon equation
Ross Parker, P. G. Kevrekidis, Alejandro Aceves
We consider the existence and spectral stability of static multi-kink structures in the discrete sine-Gordon equation, as a representative example of the family of discrete Klein-G…
Reduced dynamics for one and two dark soliton stripes in the defocusing nonlinear Schrödinger equation: a variational approach
L. A. Cisneros-Ake, R. Carretero-Gonzalez, P. G. Kevrekidis
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 red…