The Initial Value Problem for the Quadratic Nonlinear Klein‐Gordon Equation

Nakao Hayashi and Pavel I. Naumkin

Advances in Mathematical Physics, 2010, vol. 2010, issue 1

Abstract: We study the initial value problem for the quadratic nonlinear Klein‐Gordon equation ℒu=〈i∂x〉 -1u¯2, (t, x) ∈ R × R, u(0, x) = u0(x), x ∈ R, where ℒ = ∂t + i〈i∂x〉 and 〈i∂x〉=1-∂x2̅. Using the Shatah normal forms method, 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.

Date: 2010
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https://doi.org/10.1155/2010/504324

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2010:y:2010:i:1:n:504324

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