Determination of the Wave Field from Scattering Data

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Abstract
A recent exact multidimensional inverse-scattering method, developed for Schrödinger's equation, establishes a linear integral equation which determines the wave field at all space-time points from the scattering data. We present a new derivation of this integral equation which depends only on very general features of the scattering process such as causality, linearity, and the far-field decay of the wave field. Consequently, this integral equation is shown to hold for a wide class of wave equations (including, for example, the acoustic wave equation).