# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 37 (2008) pp.647-667

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### Abstract

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.

MSC(Primary) 35L70 35L15 systems of Klein Gordon equations, scattering problem, one dimension.