ON THE PARAMETRIZATION OF FINITE-GAP SOLUTIONS BY FREQUENCY AND WAVE-NUMBER VECTORS AND A THEOREM OF KRICHEVER,I

We discuss the parametrization of real finite-gap solutions of an integrable equation by frequency and wavenumber vectors. This parametrization underlies perturbation and averaging theories for the finite-gap solutions. Out of the framework of integrable equations, the parametrization gives a convenient coordinate system on the corresponding manifold of Riemann curves.