Up-down Decoupling and Paraxial Wave Equation Estimates
نویسندگان
چکیده
We provide estimates for the error incurred when a wave field produced by a directional source localized within a given plane is approximated by decoupled evolution equations describing the portions of the field moving upward and downward. The evolution equations are either pseudodifferential or of Schrödinger type (i.e. the so-called paraxial approximation) although in the latter case we must work in boundary normal coordinates. Along the way to these results we also study some microlocal, or directional, energy estimates for such wave fields which bound the energy of the wave at specific locations propagating in given directions.
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