Nonlinear scattering for a system of one dimensional nonlinear Klein–Gordon equations

Nakao Hayashi; Pavel I. Naumkin

doi:10.14492/hokmj/1249046362

Nonlinear scattering for a system of one dimensional nonlinear Klein–Gordon equations

Nakao Hayashi, Pavel I. Naumkin

SCI - Mathematics

Universidad Nacional Autónoma de México

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

Abstract

We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities (∂²_t − ∂²_x + m²_j)u>_j = N_j(∂u), j = 1, …, l. We show the existence of solutions in an analytic function space. When the nonlinearity satisfies a strong null condition introduced by Georgiev we prove the global existence and obtain the large time asymptotic behavior of small solutions.

Original language	English
Pages (from-to)	647-667
Number of pages	21
Journal	Hokkaido Mathematical Journal
Volume	37
Issue number	4
DOIs	https://doi.org/10.14492/hokmj/1249046362
Publication status	Published - 2008

Keywords

One dimension
Scattering problem
Systems of Klein Gordon equations

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abstract = "We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities (∂2t − ∂2x + m2j)u>j = Nj(∂u), j = 1, …, l. We show the existence of solutions in an analytic function space. When the nonlinearity satisfies a strong null condition introduced by Georgiev we prove the global existence and obtain the large time asymptotic behavior of small solutions.",

keywords = "One dimension, Scattering problem, Systems of Klein Gordon equations",

author = "Nakao Hayashi and Naumkin, {Pavel I.}",

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AU - Naumkin, Pavel I.

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AB - We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities (∂2t − ∂2x + m2j)u>j = Nj(∂u), j = 1, …, l. We show the existence of solutions in an analytic function space. When the nonlinearity satisfies a strong null condition introduced by Georgiev we prove the global existence and obtain the large time asymptotic behavior of small solutions.

KW - One dimension

KW - Scattering problem

KW - Systems of Klein Gordon equations

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JO - Hokkaido Mathematical Journal

JF - Hokkaido Mathematical Journal

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ER -

Nonlinear scattering for a system of one dimensional nonlinear Klein–Gordon equations

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Keywords

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