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Nonlinear scattering for a system of one dimensional nonlinear Klein-Gordon equations. (English) Zbl 1172.35454
Summary: We consider a system of nonlinear Klein-Gordon equations in one space dimension with quadratic nonlinearities
$(\partial^2_t-\partial^2_x+m^2_j)u_j={\mathcal N}_j(\partial u),$
$$j = 1,\dots,l$$. 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:
 35L70 Second-order nonlinear hyperbolic equations 35L15 Initial value problems for second-order hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs 35L55 Higher-order hyperbolic systems