On the wave turbulence theory for a stochastic KdV type equation--Generalization for the inhomogeneous kinetic limit
Starting from a stochastic Zakharov-Kuznetsov (ZK) equation on a lattice, the previous work
[ST21] by the last two authors gave a derivation of the homogeneous 3-wave kinetic …
[ST21] by the last two authors gave a derivation of the homogeneous 3-wave kinetic …
Optimal local well-posedness theory for the kinetic wave equation
We prove local existence and uniqueness results for the (space-homogeneous) 4-wave
kinetic equation in wave turbulence theory. We consider collision operators defined by …
kinetic equation in wave turbulence theory. We consider collision operators defined by …
On the wave turbulence theory for a stochastic KdV type equation
G Staffilani, MB Tran - arXiv preprint arXiv:2106.09819, 2021 - arxiv.org
Starting from the stochastic Zakharov-Kuznetsov equation, a multidimensional KdV type
equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We …
equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We …
[图书][B] Statistical physics of non equilibrium quantum phenomena
The transition from Newtonian mechanics to quantum mechanics in the early years of the
twentieth century was a major step in the progress of our understanding of the world. This …
twentieth century was a major step in the progress of our understanding of the world. This …
Almost sharp wave kinetic theory of multidimensional KdV type equations with
X Ma - arXiv preprint arXiv:2204.06148, 2022 - arxiv.org
In this work, we study the random series expansion of a multidimensional KdV type equation
with a diffusion term, the so-called Zakharov-Kuznetsov (ZK) equation. We impose random …
with a diffusion term, the so-called Zakharov-Kuznetsov (ZK) equation. We impose random …
On the wave turbulence theory for stratified flows in the ocean
After the pioneering work of Garrett and Munk, the statistics of oceanic internal gravity waves
has become a central subject of research in oceanography. The time evolution of the …
has become a central subject of research in oceanography. The time evolution of the …
On the wave turbulence theory: ergodicity for the elastic beam wave equation
Inspiring by a recent work [57], we analyse a 3-wave kinetic equation, derived from the
elastic beam wave equation on the lattice. The ergodicity condition states that two distinct …
elastic beam wave equation on the lattice. The ergodicity condition states that two distinct …
A new paradigm for scattering theory of linear and nonlinear waves: review and open problems
A Soffer - Advances in Continuous and Discrete Models, 2024 - Springer
I present a review of the recent advancements in scattering theory, which provides a unified
approach to studying dispersive and hyperbolic equations with general interaction terms …
approach to studying dispersive and hyperbolic equations with general interaction terms …
On the kinetic equation in Zakharov's wave turbulence theory for capillary waves
The wave turbulence equation is an effective kinetic equation that describes the dynamics of
wave spectra in weakly nonlinear and dispersive media. Such a kinetic model was derived …
wave spectra in weakly nonlinear and dispersive media. Such a kinetic model was derived …
Uniform in time lower bound for solutions to a quantum boltzmann equation of bosons
In this paper, we consider a quantum Boltzmann equation, which describes the interaction
between excited atoms and a condensate. The collision integrals are taken–over energy …
between excited atoms and a condensate. The collision integrals are taken–over energy …