Energy dependent Schrödinger operators and complex Hamiltonian systems on Riemann surfaces
By: Mark S. Alber, Gregory G. Luther, Jerold E. Marsden.
Contributors: Luther, Gregory G.; Marsden, Jerrold E.; Hewlett-Packard Laboratories.
Series: [Technical report] / HP Laboratories Bristol. Basic Research Institute in the Mathematical Sciences -- HPL-BRIMS-96-20.; BRIMS technical report -- HPL-BRIMS-96-20.
Publisher: Hewlett Packard
Published: 1996
Place of publication: Bristol [England]
Language: eng
Number of pages: 23
Subjects: Schrödinger operator; Hamiltonian systems
Other titles: Schrödinger operators and complex Hamiltonian systems.
Description: Abstract: "We use so-called energy dependent Schrödinger operators to establish a link between special classes of solutions of N-component systems of evolution equations and finite dimensional Hamiltonian systems on the moduli spaces of Riemann surfaces. We also investigate the phase space geometry of these Hamiltonian systems and introduce deformations of the level sets associated to conserved quantities, which results in a new class of solutions with monodromy for N-component systems of pde's. After constructing a variety of mechanical systems related to the spatial flows of nonlinear evolution equations, we investigate their semiclassical limits. In particular, we obtain semiclassical asymptotics for the Bloch eigenfunctions of the energy dependent Schrödinger operators, which is of importance in investigating zero-dispersion limits of N-component systems of pde's."
Notes: Cover title.

"August, 1996."

Includes bibliographical references.

Supported in part by the NSF. DMS 9403861 ; 9508711 ; 9302992.

Supported in part by BRIMS, Hewlett-Packard Labs.