The nonlinear Schrödinger equation with white noise dispersion

Anne de Bouard; Arnaud Debussche

doi:10.1016/j.jfa.2010.04.002

The nonlinear Schrödinger equation with white noise dispersion

Anne de Bouard
, Arnaud Debussche

ENS Paris-Saclay

Research output: Contribution to journal › Article › peer-review

Abstract

Under certain scaling the nonlinear Schrödinger equation with random dispersion converges to the nonlinear Schrödinger equation with white noise dispersion. The aim of this work is to prove that this latter equation is globally well posed in L² or H¹. The main ingredient is the generalization of the classical Strichartz estimates. Additionally, we justify rigorously the formal limit described above.

Original language	English
Pages (from-to)	1300-1321
Number of pages	22
Journal	Journal of Functional Analysis
Volume	259
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2010.04.002
Publication status	Published - 1 Sept 2010

Keywords

Nonlinear fibre optics
Stochastic partial differential equation
Strichartz estimates
White noise dispersion

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10.1016/j.jfa.2010.04.002

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title = "The nonlinear Schr{\"o}dinger equation with white noise dispersion",

abstract = "Under certain scaling the nonlinear Schr{\"o}dinger equation with random dispersion converges to the nonlinear Schr{\"o}dinger equation with white noise dispersion. The aim of this work is to prove that this latter equation is globally well posed in L2 or H1. The main ingredient is the generalization of the classical Strichartz estimates. Additionally, we justify rigorously the formal limit described above.",

keywords = "Nonlinear fibre optics, Stochastic partial differential equation, Strichartz estimates, White noise dispersion",

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year = "2010",

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T1 - The nonlinear Schrödinger equation with white noise dispersion

AU - de Bouard, Anne

AU - Debussche, Arnaud

PY - 2010/9/1

Y1 - 2010/9/1

N2 - Under certain scaling the nonlinear Schrödinger equation with random dispersion converges to the nonlinear Schrödinger equation with white noise dispersion. The aim of this work is to prove that this latter equation is globally well posed in L2 or H1. The main ingredient is the generalization of the classical Strichartz estimates. Additionally, we justify rigorously the formal limit described above.

AB - Under certain scaling the nonlinear Schrödinger equation with random dispersion converges to the nonlinear Schrödinger equation with white noise dispersion. The aim of this work is to prove that this latter equation is globally well posed in L2 or H1. The main ingredient is the generalization of the classical Strichartz estimates. Additionally, we justify rigorously the formal limit described above.

KW - Nonlinear fibre optics

KW - Stochastic partial differential equation

KW - Strichartz estimates

KW - White noise dispersion

U2 - 10.1016/j.jfa.2010.04.002

DO - 10.1016/j.jfa.2010.04.002

M3 - Article

AN - SCOPUS:77953361370

SN - 0022-1236

VL - 259

SP - 1300

EP - 1321

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 5

ER -

The nonlinear Schrödinger equation with white noise dispersion

Abstract

Keywords

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