Panayotis Panayotaros

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We use a time dependent modification of the Kermack and McKendrick model to study the evolution of the influenza A(H1N1)v epidemic reported in the Mexico City area under the control measures used during April and May 2009. The model illustrates how the sanitary measures postponed the peak of the epidemic and decreased its intensity. It provides quantitative(More)
We investigate Birkhoff normal forms for the periodic nonlinear Schrödinger equation with dispersion management. The normalization we describe is related to averaging arguments considered in the literature, and has the advantage of producing fewer resonant couplings between high spatial frequency modes. One consequence is that the normal form equations have(More)
We study the stability of breather solutions of a dissipative cubic discrete NLS with localized forcing. The breathers are similar to the ones found for the Hamiltonian limit of the system. In the case of linearly stable multi-peak breathers the combination of dissipation and localized forcing also leads to stability, and the apparent damping of internal(More)
We study the stability of a class of traveling waves in a model of weakly nonlinear water waves on the sphere. The model describes free surface potential flow of a fluid layer surrounding a gravitating sphere, and the evolution equations are Hamiltonian. For small amplitude oscillations the Hamiltonian can be expanded in powers of the wave amplitude,(More)
1. Juan Abad (University of Texas, Austin): Renormalization and Periodic Orbits in Hamiltonian Systems Abstract: We consider a renormalization group transformation R for analytic Hamiltonians in two or more dimensions, and use this transformation to construct invariant tori, as well as sequences of periodic orbits with rotation vectors approaching that of(More)
We consider a system of coupled nonlinear Schrödinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions’s Concentration Compactness principle to show the existence of standing waves with prescribed L2 norm in an averaged equation that approximates the coupled system. We also use(More)
The behavior of large-scale vortices governed by the discrete nonlinear Schrödinger equation is studied. Using a discrete version of modulation theory, it is shown how vortices are trapped and stabilized by the self-consistent Peierls-Nabarro potential that they generate in the lattice. Large-scale circular and polygonal vortices are studied away from the(More)
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