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

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study the initial value problem for the quadratic nonlinear Klein-Gordon equation Lu = 〈i∂x-1 u-2, (t,x) ∈ R × R, u(0,x ) = u0(x), x ∈ R, where L = ∂t + i〈i∂x 〉 and 〈i∂ x〉 = 1 - ∂2 x. 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.

Original languageEnglish
Article number504324
JournalAdvances in Mathematical Physics
DOIs
Publication statusPublished - 2010

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Applied Mathematics

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