Publications associées à Onde cnoïdale

Soliton gas: Theory, numerics, and experiments

The concept of soliton gas was introduced in 1971 by Zakharov as an infinite collection of weakly interacting solitons in the framework of Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted (rarefied) soliton gas, solitons with ...

Amer Physical Soc2024

Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations

Michele Dolce

We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size & epsilon;. Under the classical Miles-Howard stability condition on the Richardso ...

WILEY2023

Swirling against the forcing: Evidence of stable counterdirected sloshing waves in orbital-shaken reservoirs

François Gallaire, Alessandro Bongarzone, Alice Evelyne Julienne Marcotte

We investigate the response of the free liquid surface in a partially filled circular cylindrical container undergoing a planar elliptic and time-periodic orbit while maintaining fixed its orientation. For small forcing amplitudes and deep liquid layers, w ...

Amer Physical Soc2023

Dissipative Solitons and Switching Waves in Dispersion-Modulated Kerr Cavities

Tobias Kippenberg, Rui Ning Wang, Aleksandr Tusnin, Alisa Davydova, Miles Henry Anderson, Alexey Tikan

We theoretically and experimentally investigate the formation of dissipative coherent structures in Kerr nonlinear optical microresonators, whose spectrum encompasses an integrated dispersion that exceeds the cavity free-spectral range. We are able to acce ...

American Physical Society2023

Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

Maria Colombo, Silja Noëmi Aline Haffter

We consider the defocusing nonlinear wave equation ❑u D jujp ⠀1u in R3 ⠂ & UOELIG;0; 1/. We prove that for any initial datum with a scaling-subcritical norm bounded by M0 the equation is globally well-posed for p D 5 C i, where i 2 .0; ...

MATHEMATICAL SCIENCE PUBL2023

Zero dispersion Kerr solitons in optical microresonators

Tobias Kippenberg, Junqiu Liu, Wenle Weng, Miles Henry Anderson, Alexey Tikan

Solitons are shape preserving waveforms that are ubiquitous across nonlinear dynamical systems from BEC to hydrodynamics, and fall into two separate classes: bright solitons existing in anomalous group velocity dispersion, and switching waves forming 'dark ...

Nature Research2022

Emergent nonlinear phenomena in a driven dissipative photonic dimer

Tobias Kippenberg, Rui Ning Wang, Hairun Guo, Mikhail Churaev, Junqiu Liu, Alexey Tikan, Kenichi Komagata

Collective effects leading to spatial, temporal or spatiotemporal pattern formation in complex nonlinear systems driven out of equilibrium cannot be described at the single-particle level and are therefore often called emergent phenomena. They are characte ...

NATURE RESEARCH2021

Koopman Analysis of Isolated Fronts and Solitons

Jeremy Peter Parker

A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyze nonlinear dynamical systems brings new strategies for prediction and control, w ...

2020

Gravity Wave Excitation during the Coastal Transition of an Extreme Katabatic Flow in Antarctica

Alexis Berne, Etienne Gabriel Henri Vignon

The offshore extent of Antarctic katabatic winds exerts a strong control on the production of sea ice and the formation of polynyas. In this study, we make use of a combination of ground-based remotely sensed and meteorological measurements at Dumont d'Urv ...

2020

Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

2020