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Carroll, Robert Chang, Jen-Hsu 2015-09-28T15:20:24Z 2015-09-28T15:20:24Z 10000-01-01 1998 1998 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. Made available in DSpace on 2015-09-28T15:20:24Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9912209.pdf: 3128967 bytes, checksum: 2918769a0e52935ad7d5290014512234 (MD5) Previous issue date: 1998 Embargo set by: Seth Robbins for item 88248 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 77 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1998. http://hdl.handle.net/2142/86967 (MiAaPQ)AAI9912209 eng Mathematics Whitham Equations, Dispersionless KP Theory and Seiberg-Witten Variables text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.