Stability of Breathers for a Periodic Klein-Gordon Equation.

The existence of breather-type solutions, i.e., solutions that are periodic in time and exponentially localized in space, is a very unusual feature for continuum, nonlinear wave-type equations.

Discrete breathers in Klein-Gordon lattices: A deflation-based approach.

Deflation is an efficient numerical technique for identifying new branches of steady state solutions to nonlinear partial differential equations. Here, we demonstrate how to extend deflation to discover new periodic orbits in nonlinear dynamical lattices. We employ our extension to identify discrete breathers, which are generic exponentially localized, time-periodic solutions of such lattices.

Vaccination compartmental epidemiological models for the delta and omicron SARS-CoV-2 variants.

We explore the inclusion of vaccination in compartmental epidemiological models concerning the delta and omicron variants of the SARS-CoV-2 virus that caused the COVID-19 pandemic. We expand on our earlier compartmental-model work by incorporating vaccinated populations. We present two classes of models that differ depending on the immunological properties of the variant.

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 between waveguides is periodically modulated. Numerical experiments with single-site initial conditions show that, depending on the power, the system exhibits two fundamentally different behaviors. At low power, initial conditions with intensity concentrated in a single site give rise to transport, with the energy moving unidirectionally along the lattice, whereas high-power initial conditions yield stationary solutions.

The Role of Mobility in the Dynamics of the COVID-19 Epidemic in Andalusia.

Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e.