Abstract
We study the initial value problem for the quadratic nonlinear Klein‐Gordon equation , (t, x) ∈ R × R, u(0, x) = u0(x), x ∈ R, where ℒ = ∂t + i〈i∂x〉 and . 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.
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