Abstract
Algebraic geometrical solutions of a new shallow-water equationand Dym-type equation are studied in connection with Hamiltonianflows on nonlinear subvarieties of hyperelliptic Jacobians.These equations belong to a class of N-component integrablesystems generated by Lax equations with energy-dependentSchrödinger operators having poles in the spectral parameter.The classes of quasi-periodic and soliton-type solutions ofthese equations are described in terms of theta- andtau-functions by using new parametrizations. A qualitativedescription of real-valued solutions is provided.
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