Related papers: Reflection of conormal pulse solutions to large va…
In this work we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, we study robustness and existence of exponential dichotomies for nonautonomous…
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
Continuum kinetic simulations of plasmas, where the distribution function of the species is directly discretized in phase-space, permits fully kinetic simulations without the statistical noise of particle-in-cell methods. Recent advances in…
We show that photons subject to a spatially inhomogeneous electromagnetic field can experience quantum reflection. Based on this observation, we propose quantum reflection as a novel means to probe the nonlinearity of the quantum vacuum in…
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the…
The origin of 1D spirals or antisymmetric 1D pulses is explaind so far on the basis of multistability of spatially inhomogeneous and temporally oscillatory phases and so called nonvariational effects. Thus, coupled amplitude equations which…
Asymptotic couplings by reflection are constructed for a class of non-linear monotone SPDES (stochastic partial differential equations). As applications, the gradient/H\"older estimates as well as the exponential convergence are derived for…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this…
Solutions analogous to the Weber-Wheeler cylindrical pulse waves are found for the case of cylindrical gravitational waves in an expanding universe. These pulse solutions mimic the asymptotic properties of waves from an isolated source in…
This work addresses the response functions for infinite beams and plates with a force excitation at the origin of the coordinate system and its application to time reversal and time frequency analysis. The response function for…
We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries,…
In this paper, we consider the Cauchy problem for the semilinear beam equation in the subcritical case. We prove an asymptotic stability result of self-similar solutions of the associated parabolic problem. The proof of our results are…
We demonstrate numerically a method of focusing two-photon field inside one-dimensional random media. The approach is based on coherent control of backscattering achieved by adaptive spectral pulse shaping. The spectral phases of a…
Despite the apparent simplicity, the problem of refraction of electromagnetic waves at the planar interface between two media has an incredibly rich spectrum of unusual phenomena. An example is the paradox that occurs when an…
In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the…
In this Letter, we employ the complex screen method to investigate the dynamic evolution of partially coherent pulses with specified properties as they propagate through a nonlinear Kerr medium. Our results reveal that partially coherent…
In this paper we continue the study of non-diagonalisable hyperbolic systems with variable multiplicity started by the authors in \cite{Garetto2018}. In the case of space dependent coefficients, we prove a representation formula for…
Motivated by problems arising in geometric flows, we prove several regularity results for systems of local and nonlocal equations, adapting to the parabolic case a neat argument due to Caffarelli. The geometric motivation of this work comes…