Nonlinear scattering for a system of one dimensional nonlinear Klein-Gordon equations

Abstract

We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities

(∂_t²+∂_x²+ m_j²)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.