The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity

Clément Gallo

doi:10.1080/03605300802031614

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The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity

Journal article

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The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity

Clément Gallo

Communications in Partial Differential Equations, Vol.33(5), pp.729-771

30/04/2008

DOI: https://doi.org/10.1080/03605300802031614

Abstract

Initial value problem

Nonlinear Schrödinger equations Mathematics

Dark solitons

For rather general nonlinearities, we prove that defocusing nonlinear Schrödinger equations in n (n ≤ 4), with non-vanishing initial data at infinity u 0 , are globally well-posed in u 0 + H 1. The same result holds in an exterior domain in n , n = 2 3.

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Title: The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity
Creators - without role: Clément Gallo - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
Publication Details: Communications in Partial Differential Equations, Vol.33(5), pp.729-771
Identifiers: 9944806309311
Academic Unit: Institut Montpelliérain Alexander Grothendieck - IMAG
Language: English
Resource Type: Journal article
Local Fields: hal-01960961