Hamiltonian methods in the theory of solitons

Autor*innen

• Ljudvig D. Faddeev

Parameter

• 592 Seiten
• 21 Lesestunden

• Naturwissenschaften
• Physik

Mehr zum Buch

This book explores the foundations of the inverse scattering method and its applications to soliton theory as understood in Leningrad. Introduced by Kruskal and Zabusky in 1965, a soliton is a localized particle-like solution of a nonlinear equation, characterized by finite energy and specific features: its profile remains intact during propagation, and multiple solitons interact through elastic scattering, preserving their total number and shape. The concept of solitons has gained widespread recognition due to its universality and relevance in analyzing various processes in nonlinear media. The inverse scattering method, which serves as the mathematical foundation of soliton theory, has become a vital tool in mathematical physics for studying nonlinear partial differential equations, comparable in significance to the Fourier transform. The book emphasizes the Hamiltonian interpretation of this method, highlighting the popularity of differential geometry and Hamiltonian formalism in contemporary mathematical physics. This formalism presents the inverse scattering method in an elegant manner and establishes a connection between classical and quantum mechanics.

• Sprache: Englisch
• Erscheinungsdatum: 2007
• Einband: Paperback