Abstract.
We study the initial value problem for the cubic nonlinear Klein–Gordon equation
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.
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Hayashi, N., Naumkin, P.I. The initial value problem for the cubic nonlinear Klein–Gordon equation. Z. angew. Math. Phys. 59, 1002–1028 (2008). https://doi.org/10.1007/s00033-007-7008-8
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DOI: https://doi.org/10.1007/s00033-007-7008-8