University of Illinois Urbana-Champaign

Whitham Equations, Dispersionless KP Theory and Seiberg-Witten Variables

Chang, Jen-Hsu

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Description

Title
Whitham Equations, Dispersionless KP Theory and Seiberg-Witten Variables
Author(s)
Chang, Jen-Hsu
Issue Date
1998
Doctoral Committee Chair(s)
Carroll, Robert
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
We discuss averaging methods to get Whitham equations for the KP hierarchy and use period integrals, which correspond to SW variables, in the Whitham equations. Then we study applications of the Whitham theory and formulas involving branch points of some Riemann Surfaces associated with the KdV equation. Briefly, a Riemann surface gives rise to integrable systems via the BA function. The averaging process gives modulation parameters Tn, ai and Whitham equations which describe the deformation of moduli such as branch points. We outline and give a detailed development of the theory with a number of illustrative examples.
Graduation Semester
1998
Type of Resource
text
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http://hdl.handle.net/2142/86967

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