Complex Billiard Hamiltonian Systems and Nonlinear Waves

Alber, M. S., G. G. Luther, and J. E. Marsden

Progress in Nonlinear Differential Equations, Birkhauser, (A. S. Fokas and I.M. Gelfand, eds.)
Algebraic Aspects of Integrable Systems: in Memory of Irene Dorfman, 26, 1-16.

Abstract:

The relationships between phase shifts, monodromy effects and billiard solutions are studied in the context of Riemann surfaces for both integrable ordinary and partial differential equations. The ideas are illustrated with the three wave interaction, the nonlinear Schrödinger equation, a coupled Dym system and the coupled nonlinear Schrödinger equations.