Global existence of small solutions to a relativistic nonlinear Schrödinger equation

Anne De Bouard; Nakao Hayashi; Jean Claude Saut

doi:10.1007/s002200050191

Global existence of small solutions to a relativistic nonlinear Schrödinger equation

Anne De Bouard
, Nakao Hayashi
, Jean Claude Saut

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

Abstract

We study the Cauchy problem associated to a nonlinear Schrödinger equation modelling the self-channeling of a high power, ultra-short laser pulse in matter. The new nonlinear terms arise from relativistic effects and from the ponderomotive force. We prove global existence and uniqueness of small solutions in transverse space dimensions 2 and 3, and local existence without any smallness condition in transverse space dimension 1.

Original language	English
Pages (from-to)	73-105
Number of pages	33
Journal	Communications in Mathematical Physics
Volume	189
Issue number	1
DOIs	https://doi.org/10.1007/s002200050191
Publication status	Published - 1 Jan 1997

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title = "Global existence of small solutions to a relativistic nonlinear Schr{\"o}dinger equation",

abstract = "We study the Cauchy problem associated to a nonlinear Schr{\"o}dinger equation modelling the self-channeling of a high power, ultra-short laser pulse in matter. The new nonlinear terms arise from relativistic effects and from the ponderomotive force. We prove global existence and uniqueness of small solutions in transverse space dimensions 2 and 3, and local existence without any smallness condition in transverse space dimension 1.",

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AU - Hayashi, Nakao

AU - Saut, Jean Claude

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N2 - We study the Cauchy problem associated to a nonlinear Schrödinger equation modelling the self-channeling of a high power, ultra-short laser pulse in matter. The new nonlinear terms arise from relativistic effects and from the ponderomotive force. We prove global existence and uniqueness of small solutions in transverse space dimensions 2 and 3, and local existence without any smallness condition in transverse space dimension 1.

AB - We study the Cauchy problem associated to a nonlinear Schrödinger equation modelling the self-channeling of a high power, ultra-short laser pulse in matter. The new nonlinear terms arise from relativistic effects and from the ponderomotive force. We prove global existence and uniqueness of small solutions in transverse space dimensions 2 and 3, and local existence without any smallness condition in transverse space dimension 1.

UR - https://www.scopus.com/pages/publications/0009101525

U2 - 10.1007/s002200050191

DO - 10.1007/s002200050191

M3 - Article

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SN - 0010-3616

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

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Global existence of small solutions to a relativistic nonlinear Schrödinger equation

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