We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities (∂2t − ∂2x + m2j)u>j = Nj(∂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.
- One dimension
- Scattering problem
- Systems of Klein Gordon equations