Concept

Lax pair

Publications associées (13)

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 PORTFOLIO2022

Koopman Analysis of Isolated Fronts and Solitons

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

Response of noise-amplifier flows: From linear control to nonlinear jet breakup

Isha Shukla

Among hydrodynamically unstable flows, the amplifier-flows are characterized by their large amplification potential in presence of external noise. Since amplifiers do not have an intrinsic dynamics, a chosen forcing can be applied to eventually control the ...

EPFL2019

Circadian clock- and feeding-dependent regulation of translation initiation and elongation in the liver

Cédric Gobet

Circadian rhythms allow organisms to anticipate and adapt to periodic environmental changes related to the day-night cycle. These rhythms originate from a genetic network ticking in almost every cell of our body and the coordination between different organ ...

EPFL2018

Criteria for the existence of a potential well

Charles Stuart

We consider a critical point u(0) of a functional f is an element of C-1 (H, R), where H is a real Hilbert space, and formulate criteria ensuring that u(0) lies in a potential well of f without supposing that f' is Frechet differentiable at u(0). The deriv ...

Pergamon-Elsevier Science Ltd2017

Nonlinear Eigenvalue Problems With Specified Eigenvalues

Daniel Kressner

This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T, we are concerned with finding the minimal backward error such that T has a set of prescribed eigenvalues with prescribed al ...

Siam Publications2014

A class of Neumann type systems and its application

Jinbing Chen

A class of Neumann type systems are derived separating the spatial and temporal variables for the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation and the modified Korteweg-de Vries (mKdV) hierarchy. The Lax-Moser matrix of Neumann type s ...

International Press2012

Optimally Localized Wavelets and Smoothing Kernels

Kunal Narayan Chaudhury

It is well-known that the Gaussian functions and, more generally, their modulations-translations (the Gabor functions) have the unique property of being optimally localized in space and frequency in the sense of Heisenberg's uncertainty principle. In this ...

EPFL2011

Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions

Feride Tiglay

We study a family of equations defined on the space of tensor densities of weight lambda on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been iden ...

Springer Verlag2010

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Michaël Unser, Kunal Narayan Chaudhury

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized sc ...

IEEE2009

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