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Physical interpretation and stability of paraxial boundary conditions


 We derive in this paper the dynamic impedance matrices associated with some paraxial boundary conditions for wave motions in unbounded homogenous elastic media and use them to establish the existence of directions of propagation of waves for which the boundaries supply rather than dissipate energy. Also, we explore the existence of solutions of exponential growth and discuss conditions under which they can arise. These considerations may be used to provide a physical interpretation to the paraxial boundaries and to understand possible sources of instability that can develop in time-domain implementations of these schemes with finite differences.