Geometric and Quantum Aspects of Integrable Systems

The survey articles on integrable systems give a comprehensive survey of modern research in this area. Algebraic and geometric aspects are dealt with, as are non-linear equations, hierarchies of equations, and quantum groups.

Isospectral flow and Liouville-Arnold integration in loop algebrast.- Geometry of the modified KdV equation.- Integrable hierarchies and quantum gravity.- A geometric construction of solutions of the Toda lattice hierarchy.- to random matrices.- The geometry of elastic waves propagating in an anisotropic elastic medium.- Mathematical addenda to hopper's model of plane stokes flow driven by capillarity on a free surface.- Quantization of integrable mappings.- Some aspects of the q-deformed oscillator algebras as quantum groups.