Hayashi Nakao, Pavel Naumkin I.,
Nonlinear scattering for a system of one dimensional nonlinear Klein-Gordon equations.
Hokkaido Mathematical Journal, 37 (2008) pp.647-667
We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities \[(∂_t^2+∂_x^2+ m_j^2)u_j = N_j (∂u),\] $j = 1, . . . , l$. We show the existence of solutions in an analytic function space. When the nonlinearity satisfies a strong null condition introduced by Georgiev we prove the global existence and obtain the large time asymptotic behavior of small solutions.
|Uncontrolled Keywords||systems of Klein Gordon equations, scattering problem, one dimension.|