HP Labs Technical Reports

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Complex Billiard Hamiltonian Systems and Nonlinear Waves

Alber, Mark S.; Luther, Gregory G.; Marsden, Jerrold E.


Keyword(s): phase shift; monodromy; nonlinear Schrodinger; coupled dym; three waves; billiard; soliton

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 Schrodinger equation, a coupled Dym system and the coupled nonlinear Schrodinger equations.

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