Hokkaido Mathematical Journal

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

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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
MSC(Secondary)35L15
Uncontrolled Keywordssystems of Klein Gordon equations, scattering problem, one dimension.