Soliton Equations and Their Algebro-Geometric Solutions

Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl0521753082, 9780521753081, 9780511429842

As a partner to Volume 1: Dimensional Continuous Models, this book provides a self-contained introduction to solition equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices.

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Table of contents :
9780521753081pre_pi-x……Page 1
9780521753081int_p1-24……Page 11
9780521753081c01_p25-160……Page 35
9780521753081c02_p161-185……Page 171
9780521753081c03_p186-323……Page 196
9780521753081apxA_p324-352……Page 334
9780521753081apxB_p353-364……Page 363
9780521753081apxC_p365-384……Page 375
9780521753081apxD_p385-394……Page 395
9780521753081los_p395-397……Page 405
9780521753081bib_p398-422……Page 408
9780521753081ind_p423-425……Page 433
9780521753081era_p426-438……Page 436