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The description of the transport of cosmic rays in magnetized media is central to both acceleration and propagation of these particles in our Galaxy and outside. The investigation of the process of particle acceleration, especially at shock…
We analyze the spread of a localized peak of energy into vacuum for nonlinear diffusive processes. In contrast with standard diffusion, the nonlinearity results in a compact wave with a sharp front separating the perturbed region from…
It is shown that under certain dynamical conditions a material wave packet displays coherent, non-dispersive accelerated evolution in gravitational field over a modulated atomic mirror. The phenomenon takes place as a consequence of…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
We investigate the linearized hydrodynamic equations of interacting self-propelled particles in two dimensional space. It is found that the small perturbations of density and polarization fields satisfy the hyperbolic partial differential…
We study nonlinear dispersive wave systems described by hyperbolic PDE's in R^{d} and difference equations on the lattice Z^{d}. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…
Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This nonlinear process adds to the nonlinear modification of the shock due to the dynamical reaction of the…
We consider the propagation of wave packets for a nonlinear Schr\"odinger equation, with a matrix-valued potential, in the semi-classical limit. For a matrix-valued potential, Strichartz estimates are available under long range assumptions.…
The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary…
We consider the propagation of nonlinear plane waves in porous media within the framework of the Biot-Coussy biphasic mixture theory. The tortuosity effect is included in the model, and both constituents are assumed incompressible…
We study the propagation of ultra-short pulses in a cubic nonlinear medium. Using multiple-scale technique, we derive a new wave equation that preserves the nonlocal dispersion present in Maxwell's equations. As a result, we are able to…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is…
We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of small-amplitude solutions is driven by the nonlinear term. If the potential…
The generation and evolution of nonlinear waves in microwave amplifiers such as travelling wave tubes, free electron lasers and klystrons have been studied. The analysis is based on the hydrodynamic and field equations for the…
We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature…