Geometric and Quantum Aspects of Integrable Systems: Proceedings of the Eighth Scheveningen Conference Scheveningen, The Netherlands, August 16–21, 1992

J. Harnad (auth.), G. F. Helminck (eds.)3540573658, 9783540573654, 0387573658

This is a collection of review papers on integrable systems from the Eighth Scheveningen Conference on Geometric and Quantum Aspects of Integrable Systems. It gives the algebraic geometric aspects of the subject, describes integrability techniques, for examplefor the modified KdV equation, integrability of Hamiltonian systems, hierarchies of equations, probability distribution of eigenvalues, and modern aspects of quantum groups. It addresses researchers in mathematics and mathematical physics.

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Table of contents :
Isospectral flow and Liouville-Arnold integration in loop algebrast….Pages 1-42
Geometry of the modified KdV equation….Pages 43-65
Integrable hierarchies and quantum gravity….Pages 67-89
A geometric construction of solutions of the Toda lattice hierarchy….Pages 91-101
Introduction to random matrices….Pages 103-130
The geometry of elastic waves propagating in an anisotropic elastic medium….Pages 131-166
Mathematical addenda to hopper’s model of plane stokes flow driven by capillarity on a free surface….Pages 167-185
Quantization of integrable mappings….Pages 187-211
Some aspects of the q -deformed oscillator algebras as quantum groups….Pages 213-222