Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models

Front Cover
Cambridge University Press, Jun 5, 2003 - Mathematics
0 Reviews
The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and self-contained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exhaustive bibliography enhance the presentation offered in the main text.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

II
1
III
19
IV
20
V
29
VI
64
VII
88
VIII
105
IX
123
XXV
267
XXVI
283
XXVII
286
XXIX
287
XXX
293
XXXI
308
XXXII
323
XXXIII
327

XI
124
XII
134
XIII
149
XIV
173
XV
177
XVII
178
XVIII
190
XIX
212
XX
228
XXI
237
XXII
242
XXIII
243
XXIV
249
XXXIV
355
XXXV
367
XXXVI
380
XXXVII
396
XXXVIII
401
XXXIX
425
XL
445
XLI
450
XLII
466
XLIII
469
XLIV
501
Copyright

Common terms and phrases

Popular passages

Page 1 - It often happens that the understanding of the mathematical nature of an equation is impossible without a detailed understanding of its solutions. The black hole is a case in point. One could say without exaggeration that Einstein's equations of general relativity were understood only at a very superficial level before the discovery of the black hole.

References to this book

Bibliographic information