Wave operator for the system of the Dirac-Klein-Gordon equations

Nakao Hayashi, Masahiro Ikeda, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We prove the existence of the wave operator for the system of the massive Dirac-Klein-Gordon equations in three space dimensions xεR3∫ (∂t+α·∇;+iMβ)+ψ= λθβψ, (∂2t-Δ+m 2)θ=μψ*βψ, where the masses m, M>0. We prove that for the small final data φ+ ε(H 3/2+μ1)4+(θ1+, θ2+) ε H2+μ,1 with μ=5/4-5/2q and 90/37<q<6, there exists a unique global solution for system (1) with the final state conditions ∥VD,M(-t)ψ(t)-ψ +H3/2+μ1→0 and ∥VKG,m(-t) (φ(t) 〈i∇〉m-1∂tφ(t))- (φ1+ 〈i∇〉m -1φ2+)∥H2+μ1→0 as t-∞.

Original languageEnglish
Pages (from-to)896-910
Number of pages15
JournalMathematical Methods in the Applied Sciences
Issue number8
Publication statusPublished - 2011 May 30


  • Dirac-Klein-Gordon equations
  • scattering problem
  • wave operator


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