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• W1567403814 abstract "In this thesis, we discuss a geometric construction analogous to the Ward correspondence for the KP equations. We propose a Dirac operator based on the inverse scattering transform for the KP-II equation and discuss the similarities and differences to the Ward correspondence.We also consider the KP-I equation, describing a geometric construction for a certain class of solutions. We also discuss the general inverse scattering of the equation, how this is related to the KP-II equation and the problems with describing a single geometric construction that incorporates both equations.We also consider the Davey-Stewartson equations, which have a similar behaviour. We demonstrate explicitly the problems of localising the theory with generic boundary conditions. We also present a reformulation of the Dirac operator and demonstrate a duality between the Dirac operator and the first Lax operator for the DS-II equations.We then proceed to generalise the Dirac operator construction to generate other integrable systems. These include the mKP and Ishimori equations, and an extension to the KP and mKP hierarchies." @default.
• W1567403814 created "2016-06-24" @default.
• W1567403814 creator A5018546632 @default.
• W1567403814 date "1999-01-01" @default.
• W1567403814 modified "2023-09-26" @default.
• W1567403814 title "Twistor theory and the K.P. equations" @default.
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