Publications related to Cnoidal wave

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

Advanced dispersion engineering of dispersive waves in Si3N4 microresonators

Tobias Kippenberg, Junqiu Liu, Maxim Karpov, Anton Lukashchuk, Fabien Gremion

We experimentally demonstrate the possibility of dispersive wave tuning via advanced dispersion engineering. We utilize hybridized modes of concentric coupled resonators for precise control of the dispersion profile. (C) 2019 The Author(s) ...

IEEE2019

Control and stabilization of the periodic fifth order Korteweg-de Vries equation

Derek Lee Smith

We establish local exact control and local exponential stability of periodic solutions of fifth order Korteweg-de Vries type equations in H-s(& x1d54b;), s > 2. A dissipative term is incorporated into the control which, along with a propagation of regulari ...

2019

Dual comb generation in a monochromatically driven crystalline microresonator

Tobias Kippenberg, Erwan Guillaume Albert Lucas, Wenle Weng

Recent works on Kerr frequency combs demonstrated the possibility to simultaneously generate multiple soliton states with different group velocities in a single microresonator, which could be beneficial for many applications utilizing dual-comb systems. In ...

SPIE-INT SOC OPTICAL ENGINEERING2019

Polychromatic Cherenkov Radiation Induced Group Velocity Symmetry Breaking in Counterpropagating Dissipative Kerr Solitons

Tobias Kippenberg, Erwan Guillaume Albert Lucas, Wenle Weng

High-order-dispersion-induced dispersive waves emitted by dissipative Kerr solitons are frequently observed in microresonator frequency comb generation. Also known as soliton Cherenkov radiation, this type of dispersive wave plays a critical role in comb s ...

AMER PHYSICAL SOC2019

On the Modeling of Non-Vertical Risers in the Interaction of Electromagnetic Fields With Overhead Lines

Farhad Rachidi-Haeri, Marcos Rubinstein, Jun Guo

This paper proposes a simple method to take into account non-vertical risers through an equivalent partial inductance. The proposed approach was validated considering several examples and taking as reference full-wave results obtained using a numerical ele ...

2019

On Classical Global Solutions of Nonlinear Wave Equations with Large Data

Shuang Miao

This article studies the Cauchy problem for systems of semi-linear wave equations on R3+1 with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial energy. The choice of the l ...

OXFORD UNIV PRESS2019

Coupled-mode theory for stationary and nonstationary resonant sound propagation

Romain Christophe Rémy Fleury, Theodoros Koutserimpas

In this paper, we present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological coupled-mode theory. We calculate the prop ...

2019

Depth-averaged momentum equation for gravity currents with varying density: coefficient in pressure term

Mário Jorge Rodrigues Pereira Da Franca, Sara Venuleo

Gravity currents are often modelled by means of shallow water equations (SWEs). In these models, simplifications such as the consideration of a constant layer-averaged density are common. This note presents the complete and general derivation of a 2D depth ...

Taylor & Francis Ltd2018

Mid-infrared frequency comb via coherent dispersive wave generation in silicon nitride nanophotonic waveguides

Tobias Kippenberg, Hairun Guo, Camille Sophie Brès, Davide Grassani, Martin Hubert Peter Pfeiffer, Wenle Weng, Adrien Billat, Clemens Herkommer, Chuankun Zhang

Mid-infrared optical frequency combs are of significant interest for molecular spectroscopy due to the large absorption of molecular vibrational modes on the one hand, and the ability to implement superior comb-based spectroscopic modalities with increased ...

Nature Publishing Group2018

Experimental study on the hydrodynamic impact of tsunami-like waves against impervious free-standing buildings

Anton Schleiss, Michael Pfister, Davide Wüthrich, Ioan Nistor

Tsunamis, landslide-generated waves, and dam failures are rare, but highly destructive phenomena, associated with extreme loading on infrastructure. Recent events showed that specific measures must be taken to guarantee safety of both people and the built ...

2018