Wave solutions of evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians

2000/11/17 by Mark Alber, Mark S Alber, Yuri N Fedorov +1 · 5 citations
Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems

paper · doi:10.1088/0305-4470/33/47/307

openalex publication_date 2000/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

The algebraic-geometric approach is extended to study evolution equations associated with the energy-dependent Schrödinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvarieties of Jacobi varieties. The general approach is demonstrated by using new parametrizations for constructing quasi-periodic solutions of the shallow-water and Dym-type equations in terms of theta-functions. A qualitative description of real-valued solutions is provided.

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