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Complex WKB Solutions and Hamiltonian Systems on Riemann Surfaces

Alber, Mark S. ; Marsden, Jerrold E.

May, 1995

Keyword(s): Hamiltonian systems, Riemann surfaces, Shrodinger equation

Abstract: There have been many important developments in which the methods of complex and algebraic geometry have been used to investigate the eigenfunctions of Hill's operator in the context of integrable equations. In this paper we link a new class of Hamiltonian systems on Reimann surfaces to systems of pde's using Block eigenfunctions for stationary Schrodinger equations with new types of potentials. In particular, this yields a system of pde's with monodromy.

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