Abstract
The relationships between phase shifts, monodromy effects, and billiard solutions are studied in the context of Riemannian manifolds 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.
Research partially supported by NSF grants DMS 9403861 and 9508711.
GGL gratefully acknowledges support from BRIMS, Hewlett-Packard Labs and from NSF DMS under grant 9508711.
Research partially supported by NSF grant DMS 9302992.
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Alber, M.S., Luther, G.G., Marsden, J.E. (1997). Complex Billiard Hamiltonian Systems and Nonlinear Waves. In: Fokas, A.S., Gelfand, I.M. (eds) Algebraic Aspects of Integrable Systems. Progress in Nonlinear Differential Equations and Their Applications, vol 26. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2434-1_1
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