Related papers: Gurevich-Zybin system
We give the Lax representations for for the elliptic, hyperbolic and homogeneous second order Monge-Ampere equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax…
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…
The fermion generation puzzle has survived into this century as one of the great mysteries in particle physics. We consider here a possible solution within the Standard Model framework based on a nonabelian generalization of…
The second-order nonlinear optical susceptibility $\Pi^{(2)}$ for second harmonic generation is calculated for gapped graphene. The linear and second-order nonlinear plasmon excitations are investigated in context of second harmonic…
Generalized Langevin equations (GLEs) can be systematically derived via dimensional reduction from high-dimensional microscopic systems. For linear models the derivation can either be based on projection operator techniques such as the…
The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…
The response functions of a material characterize its behavior under external stimuli, such as electromagnetic radiation. Such responses may grow linearly with the amplitude of the incident radiation, as is the case of absorption, or may be…
Second-harmonic generation in resonant structures is commonly evaluated in terms of intracavity field enhancement at the fundamental and harmonic frequencies. Here, we formulate nonlinear frequency conversion within a symmetry-resolved…
We define fully non-perturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our non-linear…
We study the second-harmonic generation in left-handed metamaterials with a quadratic nonlinear response. We demonstrate a novel type of the exact phase matching between the backward propagating wave of the fundamental frequency and the…
We theoretically investigate second harmonic generation that originates from the nonlinear, magnetic Lorentz force term from single and multiple apertures carved on thick, opaque metal substrates. The linear transmission properties of…
Second harmonic generation is investigated in lithium niobate channels realized by proton exchange and quasi-phase-matched by surface periodic-poling. The reduction in conversion efficiency at high powers is interpreted in terms of…
The high-energy evolution of Wilson line operators, which at leading order is described by the Balitsky-JIMWLK equations, receives large radiative corrections enhanced by single and double collinear logarithms at next-to-leading order and…
Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…
The spontaneous transformations associated with symmetry-breaking phase transitions generate domain structures and defects that may be topological in nature. The formation of these defects can be described according to the Kibble-Zurek…
We establish global H\"older estimates for solutions to inhomogeneous linearized Monge-Amp\`ere equations in two dimensions with the right hand side being the divergence of a bounded vector field. These equations arise in the…
We generalize the idea of "extension of Hamiltonian systems" -- developed in a series of previous articles -- which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of…
We present a deep generative model, named Monge-Amp\`ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\`ere equation in optimal transport theory. The generative map from the latent space to the data space…
This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving method to construct reduced-order models. This allows to…
Previous work in the literature has studied the Hamiltonian structure of an R-squared model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. Within the framework of Dirac's theory, torsion is found to lead to a…