Type: Article

A system of quadratic nonlinear Klein-Gordon equations in 2d

Hayashi, Nakao; Naumkin, Pavel I.;

Abstract:

We consider the system of quadratic nonlinear Klein-Gordon equations {partial derivative(2)(t)nu(1) - Delta nu(1) + m(1)(2)nu(1) = nu(1)nu(2,) partial derivative(2)(t)nu(2) - Delta nu(2) + m(2)(2)v(2)= v(1)(2) in two space dimensions. Under the mass condition such that 2m(1) > m(2), we construct the scattering operator in an almost natural weighted Sobolev class H-1+delta,H- (1) or the scattering problem in lower order Sobolev class H-4/3-delta(1+delta,) (1) boolean AND H1+delta, where delta > 0 is small. (C) 2013 Elsevier Inc. All rights reserved.