Search results for "equation"

Shallow water rogue waves in nonlinear optical fibers

2013

The dynamics of extreme waves, often known as freak or rogue waves (RW), is presently a subject of intensive research. In oceanography, RW are mostly known as a sudden deep-water event which is responsible for ship wreakages and can be modeled by the 1D Nonlinear Schrodinger Equation (NLSE). In this framework, an ideal testbed is provided by optical pulse propagation in nonlinear optical fibers: extreme solitary wave emissions during supercontinuum generation or the first experimental observation of the Peregrine solitons have indeed been carried out exploiting the modulation instability occuring in fibers with anomalous dispersion.

Complex rogue wave in the fiber optics

2016

This manuscript presents the generation of complex rogue waves related to nonlinear instabilities occurring through the propagation of light in standard optical fibers. Linear and nonlinear physical phenomena involved are first listed, in particular some of them by analogy with the field of hydrodynamics. The different forms of rogue waves induced by the modulation instability process are then presented. They are also known as "breathers", and they are obtained by solving the nonlinear Schrödinger equation. From these exact solutions, various experimental systems were designed by means of numerical simulations based on two rogue-wave excitation methods. The first one is an exact generation …

Optimal Robust Quantum Control by Inverse Geometric Optimization

2020

International audience; We develop an inverse geometric optimization technique that allows the derivation of optimal and robust exact solutions of low-dimension quantum control problems driven by external fields: we determine in the dynamical variable space optimal trajectories constrained to robust solutions by Euler-Lagrange optimization; the control fields are then derived from the obtained robust geodesics and the inverted dynamical equations. We apply this method, referred to as robust inverse optimization (RIO), to design optimal control fields producing a complete or half population transfer and a NOT quantum gate robust with respect to the pulse inhomogeneities. The method is versat…

Rational solutions to the mKdV equation associated to particular polynomials

2021

International audience; Rational solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of determinants involving certain particular polynomials. This gives a very efficient method to construct solutions. We construct very easily explicit expressions of these rational solutions for the first orders n = 1 until 10.

Dynamiques de populations en milieu hétérogène : modèles et estimation de paramètres

2017

Prod 2017-344i SPE équipe EA GESTAD INRA; National audience; Cet exposé traite de (i) la modélisation de dynamiques de populations dans des paysages hétérogènes, (ii) la modélisation des paysages eux-mêmes, (iii) l'estimation des paramètres de ces modèles à partir de données d'abondance ou de données génétiques. Nous nous concentrerons sur deux grandes classes de modèles de dynamique des populations : les modèles individu-centrés basés sur des équations différentielles stochastiques, et les modèles de réaction-diffusion. Après une introduction du lien entre ces approches, 5 illustrations issues des projets sont présentées: - modélisation de paysages hétérogènes fragmentés, via l’outil MULTI…

Un modèle radiocentrique pour l'analyse des espaces ruraux périurbains

1995

Research on periurbanisation’s factors, a phenomenon that has greatly contributed to the demographic growth of French rural areas for the last twenty-five years, leads us to ask about the determinants of residential location in rural areas of people working in a town. In order to answer this question, it is necessary to transpose residential location models usually used at the scale of the town - models which are the basis of the New Urban Economics school - to periurban areas. The area we are interested in is differentiated both from urban and rural areas seen from the agricultural production point of view. But we show that it can be analyzed in the same manner as urban areas. However, thi…

A path analysis model: how liking for vegetables emerges in children

2014

A path analysis model is used to explain how preference for vegetables emerges before 2 years. It takes into account several determinants such as the child exposition, the child preferences for odors and flavors, as well as the parental behavior.

The mKdV equation and multi-parameters rational solutions

2021

Abstract N -order solutions to the modified Korteweg–de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2 N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2 N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6 .

Analysis of errors caused by incomplete knowledge of material data in mathematical models of elastic media

2011

Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation

2020

We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…