The initial value problem for the cubic nonlinear Klein-Gordon equation

Nakao Hayashi; Pavel I. Naumkin

doi:10.1007/s00033-007-7008-8

The initial value problem for the cubic nonlinear Klein-Gordon equation

Nakao Hayashi, Pavel I. Naumkin

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

69 Citations (Scopus)

Abstract

We study the initial value problem for the cubic nonlinear Klein-Gordon equation {u_tt + u-u_xx = μu³,(t, x) R × R, u(0) = u₀, u_t(0) = u₁, x R. where μ R and the initial data are real-valued functions. We obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous works.

Original language	English
Pages (from-to)	1002-1028
Number of pages	27
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	59
Issue number	6
DOIs	https://doi.org/10.1007/s00033-007-7008-8
Publication status	Published - 2008 Nov 1
Externally published	Yes

Keywords

Asymptotics of solutions
Cubic nonlinear Klein-Gordon equation
Initial value problem
The inverse wave modified operator

ASJC Scopus subject areas

Mathematics(all)
Physics and Astronomy(all)
Applied Mathematics

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10.1007/s00033-007-7008-8

Cite this

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AB - We study the initial value problem for the cubic nonlinear Klein-Gordon equation {utt + u-uxx = μu3,(t, x) R × R, u(0) = u0, ut(0) = u1, x R. where μ R and the initial data are real-valued functions. We obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous works.

KW - Asymptotics of solutions

KW - Cubic nonlinear Klein-Gordon equation

KW - Initial value problem

KW - The inverse wave modified operator

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The initial value problem for the cubic nonlinear Klein-Gordon equation

Abstract

Keywords

ASJC Scopus subject areas

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