Ms. Alber et Yn. Fedorov, Wave solutions of evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians, J PHYS A, 33(47), 2000, pp. 8409-8425
The algebraic-geometric approach is extended to study evolution equations a
ssociated with the energy-dependent Schrodinger operators having potentials
with poles in the spectral parameter, in connection with Hamiltonian flows
on nonlinear subvarieties of Jacobi varieties. The general approach is dem
onstrated by using new parametrizations for constructing quasi-periodic sol
utions of the shallow-water and Dym-type equations in terms of theta-functi
ons. A qualitative description of real-valued solutions is provided.