Soliton Equations and Their Algebro-Geometric Solutions

Sommario

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.

Riassunto

The Korteweg-de Vries (KdV), the AKNS, the nonlinear Schrödinger, the sine-Gordon and the Camassa-Holm equations, and the Thirring system, are all completely integrable nonlinear PDEs permitting special classes of solutions. This is a detailed treatment of the class of algebro-geometric solutions and their representations in terms of Riemann theta functions.

Dettagli sul prodotto

• Autori: F. Gesztesy, Fritz Gesztesy, H. Holden, Helge Holden
• Editore: Cambridge University Press
• Lingue: Inglese
• Formato: Copertina rigida
• Pubblicazione: 12.07.2016
• EAN: 9780521753074
• ISBN: 978-0-521-75307-4
• Pagine: 518
• Dimensioni: 157 mm x 235 mm x 35 mm
• Peso: 984 g
• Serie: Cambridge Studies in Advanced
• Categoria: Scienze naturali, medicina, informatica, tecnica > Matematica > Analisi