Complex geometric optics for symmetric hyperbolic systems II: nonlinear theory in one space dimension

Abstract

This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always satisfy the \emph{naive} coherence condition on the complex phases, which is required in the construction of the approximate solution. Formally the theory applies also in several space dimensions, but the \emph{naive} coherence condition appears to be too restrictive; the identification of the optimal coherence condition is still an open problem.