Symmetries and singularity structures : integrability and chaos in nonlinear dynamical systems : proceedings of the workshop, Bharathidasan University, Tiruchirapalli, India, November 29-December 2, 1989
著者
書誌事項
Symmetries and singularity structures : integrability and chaos in nonlinear dynamical systems : proceedings of the workshop, Bharathidasan University, Tiruchirapalli, India, November 29-December 2, 1989
（Research reports in physics）
Springer-Verlag, c1990
- : gw
- : us
大学図書館所蔵 件 / 全34件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
"A workshop on "Symmetries and Singularity Structure Aspects of Nonlinear Dynamical Systems" was held at Bharathidasan University" -- Pref
Includes bibliographical references and indexes
内容説明・目次
内容説明
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.
目次
I Symmetry Aspects.- Symmetries, Singularities and Exact Solutions for Nonlinear Systems.- Application of Isovector Approach for the Solutions of Differential Equations of Physical Systems.- Master Symmetries of Certain Nonlinear Partial Differential Equations.- Symmetries and Constants of Motion of Integrable Systems.- Lie Algebra, Bi-Hamiltonian Structure and Reduction Problem for Integrable Nonlinear Systems.- On the Role of Virasoro, Kac-Moody Algebra and Conformal Invariance in Soliton Hierarchies.- Generalised Lie Symmetries and Integrability of Coupled Nonlinear Oscillators with Two Degrees of Freedom.- Aspects of Symmetries of Dissipative Systems.- II Singularity Structure Aspects.- Painleve Property in Hamiltonian and Non-Hamiltonian Systems.- Singularity Structure and Chaotic Dynamics of the Parametrically Driven Duffing Oscillator.- A Singularity Analysis Approach to the Solutions of Duffing's Equation.- III Integrability and Chaos: Quantum and Classical.- Avoided Level Crossing, Solitons and Random Matrix Theory.- Random Matrices and Quantum Chaos: Effects of Symmetry-Breaking on Spectral Correlations.- Quantum Groups.- Integrable Quantum Spin Chains and Some Problems Related to Integrable Systems.- On the Quantum Inverse Problem for a New Type of Nonlinear Schroedinger Equation for Alfven Waves in Plasma.- Nonlinear Chemical Dynamics.- Dynamics of Solitons on 4He Films.- Studies on a Josephson Junction with Nonlinear Resistance.- Index of Contributors.
「Nielsen BookData」 より
