Mathematical modeling of waves in layered media near a caustic

Problems associated with the modeling of wave fields in an acoustic medium near a caustic in a nonstationary statement are considered. A mathematical model is proposed making it possible explicitly to mark a caustic as a boundary of a solution domain for an arbitrary change in the sound velocity. An effectively realizable boundary condition is established such as boundedness of the solution (pressure) on a caustic and Green’s function of a boundary-value problem is constructed. An auxiliary Goursat problem is studied and a system of its partial solutions is constructed based on hypergeometric functions. The integral Volterra equation in Green’s function is obtained and an algorithm for its expansion in the smoothness is presented. A difference scheme is proposed approximating the solution of a differential problem with an unbounded coefficient. The results of the numerical simulation are presented.