Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media

The Cauchy problem with localized initial conditions is considered for a large class of evolution equations that includes the Schrödinger and Dirac equations, Maxwell equations, linearized fluid dynamics equations, equations of the linear theory of surface water waves, equations of elasticity theory, acoustics equations, and many others. A general approach to the construction of efficient asymptotic formulas in such problems is discussed.