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University of Illinois at Urbana-Champaign
Whitham Equations, Dispersionless KP Theory and Seiberg-Witten Variables
Abstract
dc:descriptionWe 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Chang, Jen-Hsu
- Contributors dc:contributor
-
- Carroll, Robert
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI9912209
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86967