Related papers: Wave turbulence and the kinetic equation beyond le…
Unitary representations of the Galilei group are studied in phase space, in order to describe classical and quantum systems. Conditions to write in general form the generator of time translation and Lagrangians in phase space are then…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
A semi-empirical three-dimensional model of turbulence in the approximation of the far turbulent wake behind a body of revolution in a passive stratified medium is considered. The sought quantities are the kinetic turbulent energy, kinetic…
We present a link between the theory of deep water waves and that of bubble surface perturbations. Theory correspondence is shown analytically for small wavelengths in the linear regime and investigated numerically in the nonlinear regime.…
We present a nonlinear stability theory for periodic wave trains in reaction-diffusion systems, which relies on pure $L^\infty$-estimates only. Our analysis shows that localization or periodicity requirements on perturbations, as present in…
Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…
The nonlinear disturbance caused by a localised forcing moving at constant speed on the free surface of a liquid of finite depth is investigated using the forced Kadometsev-Petviashvili equation. The presence of a steady v-shaped Kelvin…
We propose a new relativistic Lorentz-invariant spin-noncommutative algebra. Using the Weyl ordering of noncommutative position operators, we build an analogue of the Moyal-Groenewald product for the proposed algebra. The Lagrange function…
In graphene, where the electron-electron scattering is dominant, electrons collectively act as a fluid. This hydrodynamic behaviour of charge carriers leads to exciting nonlinear phenomena such as solitary waves and shocks, among others. In…
We attempt to address the old problem of plane shear flows: the origin of turbulence and hence transport of angular momentum in accretion flows as well as laboratory flows, such as plane Couette flow. We undertake the problem by introducing…
The mechanism of transition from laminar state to turbulent state in Keplerian disks is still unknown. The most popular version today is generation of turbulence due to magnetorotational instability (MRI). However magnetohydrodynamic…
We present a new application of Lagrangian Perturbation Theory (LPT): the stability analysis of fluid flows. As a test case that demonstrates the framework we focus on the plane Couette flow. The incompressible Navier-Stokes equation is…
The statistical properties of a large number of weakly nonlinear waves can be described in the framework of the Weak Turbulence Theory. The theory is based on the hypothesis of an asymptotically large system. In experiments, the systems…
We study the stability/instability of the subsonic travelling waves of the Nonlinear Schr\"odinger Equation in dimension one. Our aim is to propose several methods for showing instability (use of the Grillakis-Shatah-Strauss theory, proof…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
In this paper, we study the rapid stabilization of an unstable wave equation, in which an unknown disturbance is located at the boundary condition. We address two different boundary conditions: Dirichlet- Dirichlet and Dirichlet-Neumann. In…
Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We…
We consider stochastic and deterministic three-wave semi-linear systems with bounded and almost continuous set of frequencies. Such systems can be obtained by considering nonlinear lattice dynamics or truncated partial differential…
In this work, we show that the edge dynamics of the Laughlin state in the weakly nonlinear regime is governed by the Korteweg-de Vries (KdV) equation. Our starting point is the Chern-Simons-Ginzburg-Landau theory in the lower half-plane,…
We consider front solutions of the Swift-Hohenberg equation $\partial_t u= -(1+\partial_x^2)^2 u +\epsilon ^2 u -u^3$. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using renormalization…