Reeectionless Boundary Propagation Formulas for Partial Wave Solutions to the Wave Equation
نویسندگان
چکیده
We consider solutions to the wave equation in 3+1 spacetime dimensions whose data is compactly supported at some initial time. For points outside a ball containing the initial support, we develop an outgoing wave condition, and associated one-way propagation formula, for the partial waves in the spherical-harmonic decomposition of the solution. The propagation formula expresses the l-th partial wave at time t and radius a in terms of order-l radial derivatives of the partial wave at time t ? t and radius a ? t. The boundary propagation formula can be applied to any diierential equation that is well-approximated by the wave equation outside a xed ball.
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