Symmetries and Singularity Structures
Subtitle: Integrability and Chaos in Nonlinear Dynamic Systems (Research Reports in Physics)
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG; Springer
Published: January 1991
Format: Paperback
Number of pages: 216
ISBN-13: 9783540530923
Subjects: Applied mathematics; Condensed matter physics (liquids & solids); Statistical physics
Description: These lectures deal with background and latest developments in symmetries, singularity structures (Painlevé analysis) and their relation to integrability and chaos in classical and quantum nonlinear dynamical systems. The book is useful to both newcomers and senior researchers in physics and mathematics working in the field of nonlinear dynamics. Starting from simple Lie symmetries the role of generalized Lie and Lie-Bäcklund symmetries and the underlying algebras associated with a wide spectrum of nonlinear systems are studied. Some keywords are: Master symmetries, dynamical symmetries, Kac-Moody and Virasoro algebras, quantum groups, integrable quantum spin chains, bi-Hamiltonian structure of integrable systems and singularity structure analysis of Hamiltonian and non-Hamiltonian systems, the connection between symmetry, solitons, quantum chaos and random matrix theory, applications of solitons in plasmas, 4He films, Josephson junctions and in chemical compounds.