A note on the large time asymptotics for a system of Klein-Gordon equations
Hideaki Sunagawa · Hokkaido Mathematical Journal · 2004
We study the asymptotic behavior of the solution in the large time for the system {(□ + m 2 1 )u 1 = 0 (□ + m 2 2 )u 2 = 0 (□ + m 2 3 )u 3 = u 1 u 2 in two space dimensions. We prove the existence of a solution whose amplitude is modulated by the long range effect when m 3 = λ 1 m 1 + λ 2 m 2 for some λ 1 , λ 2 ∈ {′1}.