Ms. Alber et Yn. Fedorov, Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians, INVERSE PR, 17(4), 2001, pp. 1017-1042
Algebraic geometrical solutions of a new shallow-water equation and Dym-typ
e equation are studied in connection with Hamiltonian flows on nonlinear su
bvarieties of hyperelliptic Jacobians. These equations belong to a class of
N-component integrable systems generated by Lax equations with energy-depe
ndent Schrodinger operators having poles in the spectral parameter. The cla
sses of quasi-periodic and soliton-type solutions of these equations are de
scribed in terms of theta- and tau-functions by using new parametrizations.
A qualitative description of real-valued solutions is provided.