相关论文: Resonant and Near-Resonant Internal Wave Interacti…

Nonlinear interaction and breaking of internal ocean waves are responsible for much of the interior ocean mixing, affecting ocean carbon storage and the global overturning circulation. These interactions may affect the observed Garrett-Munk…

We consider a kinetic equation describing evolution of a particle distribution function in a system with nonlinear wave-particle interactions (trappings into a resonance and nonlinear scatterings). We study properties of its solutions and…

Motivated by problems arising in geophysical fluid dynamics, we investigate resonant and near resonant wave interactions in nonlinear wave equations with quadratic nonlinearity, We place a special focus on interactions between slow wave…

Recent developments of the weak turbulence theory applied to internal waves exhibit a power-law solution of the kinetic energy equation close to the oceanic Garrett \& Munk spectrum, confirming weakly nonlinear wave interactions as a likely…

We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…

The high-frequency limit of the Garrett and Munk spectrum of internal waves in the ocean and the observed deviations from it are shown to form a pattern consistent with the predictions of wave turbulence theory. In particular, the high…

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…

As presented in Annenkov & Shrira (2009), when a surface gravity wave field is subjected to an abrupt perturbation of external forcing, its spectrum evolves on a ``fast'' dynamic time scale of $O(\varepsilon^{-2})$, with $\varepsilon$ a…

The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general…

Nonlinear triadic interactions are at the heart of our understanding of turbulence. In flows where waves are present modes must not only be in a triad to interact, but their frequencies must also satisfy an extra condition: the interactions…

We initiate the study of the asymptotic behavior of small solutions to one-dimensional Klein-Gordon equations with variable coefficient quadratic nonlinearities. The main discovery in this work is a striking resonant interaction between…

Starting from the two-dimensional Boussinesq equation without rotation, we derive a kinetic equation for weak interaction of internal waves using non-canonical variables. We follow a formalism introduced by P. Ripa in the 80's. The…

The nonlinear evolution of an ion ring instability in a low-beta magnetospheric plasma is considered. The evolution of the two-dimensional ring distribution is essentially quasilinear. Ignoring nonlinear processes the time-scale for the…

It is generally accepted that the evolution of deep-water surface gravity wave spectrum is governed by quartet resonant and quasi-resonant interactions. However, it has also been reported in both experimental and computational studies that…

This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…

Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For a system of nonlinear Klein-Gordon equations, a systematic analysis of the time evolution for their spatially uniform solutions has been performed…

The multi-wave exact resonance condition is a fundamental principle for understanding energy transfer in condensed matter systems, yet the dynamical evolution of waves satisfying this condition remains unexplored. Here, we reveal that the…

Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently…

Recently Mendonca and Cardoso [Phys. Rev. D, vol. 66, 104009 (2002)] considered nonlinear gravitational wave packets propagating in flat space-time. They concluded that the evolution equation - to third order in amplitude - takes a similar…

We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that the non-self-adjoint generator of the evolution problem…