Mathematical modelling of waves in layered media nearby a caustic

Problems of modeling of scattered wave-fields nearby a caustic in acoustic medium in a non-stationary statement are considered. The mathematical model allowing explicitly select caustic as boundary of solution domain for arbitrary change of sound speed is offered. The еffectively realized boundary condition such as limited solution (pressure) on a caustic is established and Green's function of the boundary-value problem is constructed. The auxiliary Goursat's problem is considered and, on the basis of hypergeometric functions, the system of its partial solutions is constructed. The integral Volterra equation with respect to the Green's function is received and the algorithm of its expansion in terms of smoothness is specified. We propose a finite-difference scheme approximating the solution of the differential problem with an unlimited coefficient. The results of numerical modeling are presented.