The D-bar approach to inverse scattering and nonlinear evolutions

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Abstract

The inverse scattering method for solving nonlinear equations can be considered as the inversion of a complex differential equation, the -equation. This viewpoint applies to multidimensional problems. The Davey-Stewartson and self-dual Yang-Mills equations and associated hierarchies are discussed, as well as the Schrödinger equation in R3.

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Research supported by NSF grant DMS 8402637