Related papers: GENERIC formulation and small-angle limit for Kine…
We prove quantitative scattering for the three-dimensional defocusing energy-critical quintic wave equation on a class of asymptotically flat, possibly non-stationary perturbations of Minkowski space, by establishing the first explicit…
We present a derivation using kinetic wave theory of the two-dimensional empirical Garrett--Munk spectrum for ocean internal waves, valid at all frequencies including near-inertial frequencies. This is based directly on the governing…
We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined…
We study time-periodic solutions for the cubic wave equation on an interval with Dirichlet boundary conditions. We begin by following the perturbative construction of Vernov and Khrustalev and provide a rigorous derivation of the…
In dimensions one to three, the fundamental solution to the free wave equation is positive. Therefore, there exists a simple positivity criterion for solutions. We use this to obtain large global solutions to two well-studied…
The dynamics of a massive, relativistic spinning particle could be described either by the Dirac equation or by the Kerr solution of Einstein equations. However, one does not know a priori as to which of the two systems of equations should…
We study the thermalization of the classical Klein-Gordon equation under a u^4 interaction. We numerically show that even in the presence of strong nonlinearities, the local thermodynamic equilibrium state exhibits a weakly nonlinear…
We highlight some subtleties that affect naive implementations of quadrupolar and octupolar gravitational waveforms from numerically-integrated trajectories of three-body systems. Some of those subtleties arise from the requirement that the…
We construct the gravitational-wave equation in the background of the effective one-body system for the spinless binary, which is in general available with the spherically symmetric background as well. The gauge conditions are given in…
The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation…
In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a…
Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
In this article, we consider energy-critical complex Ginzburg-Landau equation in three and four dimensions. We give the dynamics when the energy of the initial data is equal to the energy of the stationary solution.
The known nonlinear kinetic equations (in particular, the wave kinetic equation and the quantum Nordheim -- Uehling -- Uhlenbeck equations) are considered as a natural generalization of the classical spatially homogeneous Boltzmann…
We investigate the propagation of gravitational waves in the context of fourth order gravity nonminimally coupled to a massive scalar field. Using the damping of the orbital period of coalescing stellar binary systems, we impose constraints…
For the one-dimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and…
We solve Klein-Gordon equation (KGE) in the framework of the real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM). The presented solution is the simplest ever obtained for quaternionic quantum theories, and the…
We study a Hamiltonian system of type describing a charged particle resonant interaction with an electromagnetic wave. We consider an ensemble of particles that repeatedly pass through the resonance with the wave, and study evolution of the…
Generally speaking, there is a negative kinetic energy term in the Lagrangian of the Einstein-Hilbert action of general relativity; On the other hand, the negative kinetic energy term can be vanished by designating a special coordinate…