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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 twisted multi-core optical fiber. By considering an even number, N, of waveguides, we derive asymptotic expressions …

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 permutation symmetries in the network as the global coupling strength g is varied. We primarily consider two …

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 (Degasperis-Procesi) integrable examples. We establish information about the point spectrum of the peakon solutions and …

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 invariant and reversible, for which the fifth-order Korteweg-de Vries equation is a prototypical example. We use Lin's …