Fritz Gesztesy, Helge Holden

Soliton Equations and their Algebro-Geometric Solutions

• Gebundenes Buch

Produktbeschreibung

This book is about 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 and 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).

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 518
• Erscheinungstermin: 12. Juli 2016
• Englisch
• Abmessung: 235mm x 157mm x 35mm
• Gewicht: 986g
• ISBN-13: 9780521753074
• ISBN-10: 0521753074
• Artikelnr.: 22045627

Inhaltsangabe

Introduction
1. The KdV hierarchy
2. The sGmKdV hierarchy
3. The AKNS hierarchy
4. The classical massive Thirring system
5. The Camassa-Holm hierarchy
Appendix A. Algebraic curves and their theta functions
Appendix B. KdV-type curves
Appendix C. AKNS-type curves
Appendix D. Asymptotic spectral parameter expansions
Appendix E. Lagrange interpolation
Appendix F. Symmetric functions
Appendix G. KdV and AKNS Darboux-type transformations
Appendix H. Elliptic functions
Appendix I. Herglotz functions
Appendix J. Weyl-Titchmarsh theory
List of symbols
Bibliography
Index.