Transparent boundary conditions for the high-order parabolic approximations

Transparent boundary conditions for the hierarchies of parabolic equations where the solution of n-th equation is used as an input term for n+1-th equation are derived. The existence, uniqueness, and well-posedness of the initial boundary value problem for the system of coupled parabolic equations with the derived boundary conditions is established. Such coupled systems of parabolic equations can be used to approximate the solution of the Helmholtz equation. The derived transparent boundary conditions may be therefore used for the simulation of wave propagation in unbounded media.