Soliton Equations and Hamilton Systems

The theory of soliton equations and integrable systems has developed rapidly during the last 20 years with numerous applications in mechanics and physics. For a long time books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this followed one single work by Gardner, Greene, Kruskal, and Miura about the Korteweg-de Vries equation (KdV) which, had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.

Sommario

Integrable systems generated by linear differential nth order operators; Hamiltonian structures; Hamiltonian structures of the KdV-hierarchies; the Kupershmidt-Wilson theorem; the KP-hierarchy; Hamiltonian structure of the KP-hierarchy; Baker function, tau-function; Grassmannian, tau-function and Baker function after Segal and Wilson. Algebraic-geometrical Krichever's solutions; matrix first-order operators; KdV-hierarchies as reductions of matrix hierarchies; stationary equations; stationary equations of the KdV-hierarchy in the narrow sense (n=2); stationary equations of the matrix hierarchy; stationary equations of the KdV-hierarchies; matrix differential operators polynomially depending on a parameter; multi-time Lagrangian and Hamiltonian formalism; further examples and applications.

Dettagli sul prodotto

• Autori: L a Dickey, L. A. Dickey, Dickey L.A.
• Editore: Ingram Publishers Services
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 01.09.1991
• EAN: 9789810236847
• ISBN: 978-981-02-3684-7
• Pagine: 350
• Serie: Advanced Series in Mathematica; Advanced Series in Mathematica
• Categorie: Scienze naturali, medicina, informatica, tecnica > Fisica, astronomia > Tematiche generali, enciclopedie; MATHEMATICS / Applied, MATHEMATICS / Topology, Analytic topology, Applied mathematics