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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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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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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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Multi-pulse solitary waves in a fourth-order nonlinear Schrödinger equation
In the present work, we consider the existence and spectral stability of multi-pulse solitary wave solutions to a nonlinear Schrödinger …
Ross Parker, Alejandro Aceves
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A reformulated Krein matrix for star-even polynomial operators with applications
In its original formulation the Krein matrix was used to locate the spectrum of first-order star-even polynomial operators where both …
Todd Kapitula, Ross Parker, Björn Sandstede
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Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems
In the present work, we consider the existence and spectral stability of multi-pulse solutions in Hamiltonian lattice systems which are …
Ross Parker, P.G. Kevrekidis, Björn Sandstede
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