A nonlinear scattering problem

We consider neutral nearly diagonal n-dimensional systems. We study the propagation of solutions past the complete degeneracy of the linearized problem. Under several conditions we show that there exists a global solution. Our main result is an asymptotic formula. To establish this formula we use the Kolmogorov-Arnold-Moser method and the Moser-Jacobowitz approximation method to obtain a priori estimates for solutions. These a priori estimates provide a rigorous justification for our calculation of explicit asymptotic formulas by a technique of matched asymptotic expansions