Diffraction on a quadrant

Abstract

Diffraction theory, one of the most important areas of mathematical physics, has recently been under intensive development. Integral or more generally pseudodifferential equations take an exceptional place in diffraction theory; as a rule diffraction problems reduce to one or another of them [69,123,57,118]. This reduction to boundary equations is achieved by different methods, depending on the particular equation type, and the investigations in many cases lead to existence and uniqueness theorems. One of the methods used for solving the boundary equations thus attained is the Wiener-Hopf method, or the factorization method, which has been successfully applied to some diffraction problems [166­168,175,240,256,257]. We suggested here a multidimensional generalization of this method, and with its help we will study pseudodifferential equations arising from a diffraction problem on a quadrant, obtained in [168]. The solution in the simplest case of this problem can be written in explicit form and is more appealing than the formula found in [168].