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Concept

Integrable system

Related publications (31)

Soliton gas: Theory, numerics, and experiments

Andrey Gelash

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

Spectral and thermodynamic properties of interacting electrons with dynamical functionals

Tommaso Chiarotti

Empowered by ever-increasing computational power and algorithmic developments, electronic-structure simulations continue to drive research and innovation in materials science. In this context, ab-initio calculations offer an unbiased platform for the under ...

EPFL2023

Backtracking Dynamical Cavity Method

Lenka Zdeborová, Freya Behrens, Barbora Hudcová

The cavity method is one of the cornerstones of the statistical physics of disordered systems such as spin glasses and other complex systems. It is able to analytically and asymptotically exactly describe the equilibrium properties of a broad range of mode ...

American Physical Society2023

Higher-order organization of multivariate time series

Enrico Amico, Andrea Santoro

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Several methods have been proposed for the analysis of multivar ...

NATURE PORTFOLIO2023

Weak nonlinearity for strong non-normality

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they experience transient growth or respond to harmonic forcing. This approach reconciles the non-modal nature of ...

Cambridge University Press2022

Weakly nonlinear evolution of stochastically driven non-normal systems

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We consider nonlinear dynamical systems driven by stochastic forcing. It has been largely evidenced in the literature that the linear response of non-normal systems (e.g. fluid flows) may exhibit a large variance amplification, even in a linearly stable re ...

Cambridge University Press2022

Microresonator Dissipative Kerr Solitons Synchronized to an Optoelectronic Oscillator

Tobias Kippenberg, Wenle Weng, Jijun He

Using phase-modulation-induced potential gradient whose period is synchronized to a microwave opto-electronic oscillator, dissipative Kerr solitons generated in a crystalline optical microresonator are trapped by the soliton tweezing effect, exhibiting a s ...

American Physical Society (APS)2022

Protected generation of dissipative Kerr solitons in supermodes of coupled optical microresonators

Tobias Kippenberg, Junqiu Liu, Rui Ning Wang, Johann Emmeram Riemensberger, Mikhail Churaev, Xinru Ji, Alexey Tikan, Aleksandr Tusnin

A photonic dimer composed of two evanescently coupled high-Q microresonators is a fundamental element of multimode soliton lattices. It has demonstrated a variety of emergent nonlinear phenomena, including supermode soliton generation and soliton hopping. ...

AMER ASSOC ADVANCEMENT SCIENCE2022

Locally active globally stable dynamical systems: Theory, learning, and experiments

Aude Billard, Nadia Barbara Figueroa Fernandez

State-dependent dynamical systems (DSs) offer adaptivity, reactivity, and robustness to perturbations in motion planning and physical human-robot interaction tasks. Learning DS-based motion plans from non-linear reference trajectories is an active research ...

SAGE PUBLICATIONS LTD2022

Unfreezing Social Navigation: Dynamical Systems based Compliance for Contact Control in Robot Navigation

Aude Billard, Diego Felipe Paez Granados, Vaibhav Gupta

Large efforts have focused on ensuring that the controllers for mobile service robots follow proxemics and other social rules to ensure both safe and socially acceptable distance to pedestrians. Nonetheless, involuntary contact may be unavoidable when the ...

IEEE2022

Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case

Klaus Martin Widmayer

We consider the Vlasov–Poisson system with repulsive interactions. For initial data a small, radial, absolutely continuous perturbation of a point charge, we show that the solution is global and disperses to infinity via a modified scattering along traject ...

2021

Structure-Preserving Reduced Basis Methods For Poisson Systems

Jan Sickmann Hesthaven, Cecilia Pagliantini

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

AMER MATHEMATICAL SOC2021

Electromagnetic waves under nonstationary conditions, the connection with parity-time symmetry and studies on resonant systems

Theodoros Koutserimpas

In this thesis, the electromagnetic wave propagation is studied in nonstationary-medium scenarios. The electromagnetic fields under material time-modulation are shown to conserve their momentum but not their energy. The mathematical foundations and analysi ...

EPFL2021

Nonlinear reconstruction of bioclimatic outdoor-environment dynamics for the Lower Silesia region (SW Poland)

Paolo Perona

Measured meteorological time series are frequently used to obtain information 8 about climate dynamics. We use time series analysis and nonlinear system identification 9 methods in order to assess outdoor-environment bioclimatic conditions starting from th ...

2021

Positive Solutions of Transport Equations and Classical Nonuniqueness of Characteristic curves

Maria Colombo

The seminal work of DiPerna and Lions (Invent Math 98(3):511-547, 1989) guarantees the existence and uniqueness of regular Lagrangian flows for Sobolev vector fields. The latter is a suitable selection of trajectories of the related ODE satisfying addition ...

2021

Spectral multiplexing of dissipative Kerr solitons in a single optical microresonator

Tobias Kippenberg, Junqiu Liu, Maxim Karpov, Martin Hubert Peter Pfeiffer, Anton Lukashchuk

We experimentally demonstrate that dissipative Kerr solitons generated in different spectral regions can stably coexist in a single optical microresonator enabling spectral multiplexing of soliton microcombs. (C) 2020 The Author(s) ...

IEEE2020

Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Max-Olivier Hongler

he concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose ...

2020

Dynamics and Applications of Dissipative Kerr Solitons

Maxim Karpov

Optical frequency combs are optical sources, which spectrum consists of a series of equally spaced narrowband frequencies. They made an outstanding leap forward in the accuracy of optical frequency metrology and became an attractive tool for numerous appli ...

EPFL2020

Heteronuclear soliton molecules in optical microresonators

Tobias Kippenberg, Wenle Weng, Erwan Guillaume Albert Lucas, Tobias Herr, Romain Dany Bruno Bouchand

Optical soliton molecules are bound states of solitons that arise from the balance between attractive and repulsive effects. Having been observed in systems ranging from optical fibres to mode-locked lasers, they provide insights into the fundamental inter ...

Nature Research2020

Massively parallel coherent LiDAR using dissipative Kerr solitons

Tobias Kippenberg, Junqiu Liu, Maxim Karpov, Johann Emmeram Riemensberger, Erwan Guillaume Albert Lucas, Wenle Weng, Anton Lukashchuk

We demonstrate an architecture for massively parallel frequency-modulated continuous wave (FMCW) laser ranging (LiDAR) by transferring linear chirps of a single narrow linewidth laser onto all soliton comb teeth though generation of a dissipative Kerr soli ...

IEEE2020