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Standing and Traveling Waves in a Model of Periodically Modulated One-dimensional Waveguide Arrays
In the present work, we study coherent structures in a one-dimensional discrete nonlinear Schrödinger lattice in which the coupling …
Ross Parker, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Alejandro Aceves
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Kink-Antikink Interaction Forces and Bound States in a nonlinear Schrödinger Model with Quadratic and Quartic dispersion
In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of …
G.A. Tsolias, Robert J. Decker, A. Demirkaya, T.J. Alexander, Ross Parker, P.G. Kevrekidis
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The Stability of the b-family of Peakon Equations
In the present work we revisit the b-family model of peakon equations,containing as special cases the b=2 (Camassa-Holm) and b=3 …
Efstathios G. Charalampidis, Ross Parker, Panayotis G. Kevrekidis, Stéphane Lafortune
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Bifurcations of a neural network model with symmetry
We analyze a family of clustered excitatory-inhibitory neural networks and the underlying bifurcation structures that arise because of …
Ross Parker, Andrea K. Barreiro
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Revisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach
We consider the existence and spectral stability of multi-breather structures in the discrete Klein-Gordon equation, both for soft and …
Ross Parker, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Alejandro Aceves
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Spatiotemporal dynamics in a twisted, circular waveguide array
We consider the existence and spectral stability of nonlinear discrete localized solutions representing light pulses propagating in a …
Ross Parker, Yannan Shen, Alejandro Aceves, John Zweck
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Periodic multi-pulses and spectral stability in Hamiltonian PDEs with symmetry
We consider the existence and spectral stability of periodic multi-pulse solutions in Hamiltonian systems which are translation …
Ross Parker, Björn Sandstede
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Floquet solitons in square lattices: Existence, Stability and Dynamics
In the present work, we revisit a recently proposed and experimentally realized topological 2D lattice with periodically time-dependent …
Ross Parker, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Alejandro Aceves
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Stationary multi-kinks in the discrete sine-Gordon equation
We consider the existence and spectral stability of static multi-kink structures in the discrete sine-Gordon equation, as a …
Ross Parker, Panayotis G. Kevrekidis, Alejandro Aceves
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Standing wave solutions in twisted multicore fibers
In the present work, we consider the existence and spectral stability of standing wave solutions to a model for light propagation in a …
Ross Parker, Alejandro Aceves
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