Analytic regularity for solutions of nonlinear weakly hyperbolic equations

Analytic regularity of real solutions of a nonlinear weakly hyperbolic equation with characteristic roots of constant multiplicity is studied in the paper. It is proved that the analytic regularity of Cauchy data propagates according to the geometry of the influence domains of the equation if its solution is "sufficiently regular". Local propagation results are achieved as an application of a theorem concerning the continuity of a class of infinite-order Fourier integral operators in Sobolev spaces with weight of exponential type.