36 citations · 102 across the 15 of their papers we have counts for
7 papers · 1 filter
Standing and Traveling Waves in a Nonlinearly Dispersive Lattice Model
Ross Parker, Pierre Germain, Jesús Cuevas-Maraver +2
In the work of Colliander et al. (2010), a minimal lattice model was constructed describing the transfer of energy to high frequencies in the defocusing nonlinear Schrödinger equat…
Standing and Traveling Waves in a Model of Periodically Modulated One-dimensional Waveguide Arrays
Ross Parker, Jesús Cuevas-Maraver, P. G. Kevrekidis +1
In the present work, we study coherent structures in a one-dimensional discrete nonlinear Schrödinger lattice in which the coupling between waveguides is periodically modulated. Nu…
Kink-Antikink Interaction Forces and Bound States in a nonlinear Schr{ö}dinger Model with Quadratic and Quartic dispersion
G. A. Tsolias, Robert J. Decker, A. Demirkaya +3
In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schr{ö}dinger type bearing cubi…
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…
Spatiotemporal dynamics in a twisted, circular waveguide array
Ross Parker, Yannan Shen, Alejandro Aceves +1
We consider the existence and spectral stability of nonlinear discrete localized solutions representing light pulses propagating in a twisted multi-core optical fiber. By consideri…
Floquet solitons in square lattices: Existence, Stability and Dynamics
Ross Parker, Jesús Cuevas-Maraver, P. G. Kevrekidis +1
In the present work, we revisit a recently proposed and experimentally realized topological 2D lattice with periodically time-dependent interactions. We identify the fundamental so…
Multi-pulse solitary waves in a fourth-order nonlinear Schrödinger equation
Ross Parker, Alejandro Aceves
In the present work, we consider the existence and spectral stability of multi-pulse solitary wave solutions to a nonlinear Schrödinger equation with both fourth and second order d…