Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations (Q1033776)

Linear hyperbolic systems of differential equations for an m-D vector function are considered. There is a large discussion on the asymptotics of solutions to the associated Cauchy problem with fast-decaying or localized initial data. The aim is to present explicit formulas for the asymptotic solutions of the Cauchy problem. Authors concentrate and prove results for the Cauchy problem with localized initial data for the linearized shallow water equations. A main point of proofs is the possibility of representation of fast decaying functions by means of Maslov canonical operator over a specific Lagrange manifold.