Symmetries and Singularity Structures

Muthiah Daniel

ISBN 10: 3540530924 / ISBN 13: 9783540530923

Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Jan 1991, 1991

Beschreibung

Neuware -Symmetries and singularity structures play important roles in the study of nonlinear dynamical systems. It was Sophus Lie who originally stressed the importance of symmetries and invariance in the study of nonlinear differential equations. How ever, the full potentialities of symmetries had been realized only after the advent of solitons in 1965. It is now a well-accepted fact that associated with the infinite number of integrals of motion of a given soliton system, an infinite number of gep. eralized Lie BAcklund symmetries exist. The associated bi-Hamiltonian struc ture, Kac-Moody, Vrrasoro algebras, and so on, have been increasingly attracting the attention of scientists working in this area. Similarly, in recent times the role of symmetries in analyzing both the classical and quantum integrable and nonintegrable finite dimensional systems has been remarkable. On the other hand, the works of Fuchs, Kovalevskaya, Painleve and coworkers on the singularity structures associated with the solutions of nonlinear differen tial equations have helped to classify first and second order nonlinear ordinary differential equations. The recent work of Ablowitz, Ramani and Segur, con jecturing a connection between soliton systems and Painleve equations that are free from movable critical points, has motivated considerably the search for the connection between integrable dynamical systems with finite degrees of freedom and the Painleve property. Weiss, Tabor and Carnevale have extended these ideas to partial differential equations.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 224 pp. Englisch.

Bestandsnummer des Verkäufers 9783540530923

Bibliografische Details

• Titel: Symmetries and Singularity Structures
• Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Jan 1991
• Erscheinungsjahr: 1991
• Sprache: Englisch
• ISBN-10: 3540530924
• ISBN-13: 9783540530923
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 242B x 170 H x 13 T Millimeter Breite: 242 mm, Höhe: 170 mm, Tiefe: 13 mm
• Gewicht: 392 Gramm

Über diesen Titel

Inhaltsangabe

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

Reseña del editor

Proceedings of the Workshop, Bharathidasan University, Tiruchirapalli, India, November 29 - December 2, 1989