36 citations · 102 across the 15 of their papers we have counts for
15 papers
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…
Bifurcations of a neural network model with symmetry
Ross Parker, Andrea K. Barreiro
We analyze a family of clustered excitatory-inhibitory neural networks and the underlying bifurcation structures that arise because of permutation symmetries in the network as the…
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…
Distances for the RR Lyrae stars UU Ceti, UW Gruis, & W Tucanae
Ross Parker, Liam Parker, Hayden Parker +2
B, V, i, and z bandpass observations were collected in late 2020 for three RRab type stars: UU Ceti, UW Gruis, and W Tucanae. The period-luminosity (PL) relationships of Catalen et…
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…
Standing Wave Solutions in Twisted Multicore Fibers
Ross Parker, Alejando Aceves
In the present work, we consider the existence and spectral stability of standing wave solutions to a model for light propagation in a twisted multi-core fiber with no gain or loss…
The Stability of the -family of Peakon Equations
Efstathios G. Charalampidis, Ross Parker, Panayotis G. Kevrekidis +1
In the present work we revisit the -family model of peakon equations, containing as special cases the (Camassa-Holm) and (Degasperis-Procesi) integrable examples. We…
Periodic multi-pulses and spectral stability in Hamiltonian PDEs with symmetry
Ross Parker, Björn Sandstede
We consider the existence and spectral stability of periodic multi-pulse solutions in Hamiltonian systems which are translation invariant and reversible, for which the fifth-order…
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…
Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems
Ross Parker, P. G. Kevrekidis, Björn Sandstede
In the present work, we consider the existence and spectral stability of multi-pulse solutions in Hamiltonian lattice systems. We provide a general framework for the study of such…
A reformulated Krein matrix for star-even polynomial operators with applications
Todd Kapitula, Ross Parker, Björn Sandstede
In its original formulation the Krein matrix was used to locate the spectrum of first-order star-even polynomial operators where both operator coefficients are nonsingular. Such op…