Scattering operator for nonlinear klein-Gordon equations

Nakao Hayashi; Pavel I. Naumkin

doi:10.1142/S0219199709003582

Scattering operator for nonlinear klein-Gordon equations

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journal › Article

16 Citations (Scopus)

Abstract

We prove the existence of the scattering operator in H^1+n/2,1 in the neighborhood of the origin for the nonlinear KleinGordon equation with a power nonlinearity u_tt-Δu+u=μ|u|^p-1u, (t,x) ∈ R × Rⁿ, where p > 1+2/n, μ ∈ C, n=1,2.

Original language	English
Pages (from-to)	771-781
Number of pages	11
Journal	Communications in Contemporary Mathematics
Volume	11
Issue number	5
DOIs	https://doi.org/10.1142/S0219199709003582
Publication status	Published - 2009 Oct 1
Externally published	Yes

Keywords

Asymptotics of solutions
Nonlinear Klein-Gordon equation
Scattering operator

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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abstract = "We prove the existence of the scattering operator in H1+n/2,1 in the neighborhood of the origin for the nonlinear KleinGordon equation with a power nonlinearity utt-Δu+u=μ|u|p-1u, (t,x) ∈ R × Rn, where p > 1+2/n, μ ∈ C, n=1,2.",

keywords = "Asymptotics of solutions, Nonlinear Klein-Gordon equation, Scattering operator",

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AU - Naumkin, Pavel I.

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N2 - We prove the existence of the scattering operator in H1+n/2,1 in the neighborhood of the origin for the nonlinear KleinGordon equation with a power nonlinearity utt-Δu+u=μ|u|p-1u, (t,x) ∈ R × Rn, where p > 1+2/n, μ ∈ C, n=1,2.

AB - We prove the existence of the scattering operator in H1+n/2,1 in the neighborhood of the origin for the nonlinear KleinGordon equation with a power nonlinearity utt-Δu+u=μ|u|p-1u, (t,x) ∈ R × Rn, where p > 1+2/n, μ ∈ C, n=1,2.

KW - Asymptotics of solutions

KW - Nonlinear Klein-Gordon equation

KW - Scattering operator

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