Bounded ultra-elliptic solutions of the defocusing nonlinear Schrödinger equation

An effective integration method is presented for the bounded ultra-elliptic solutions of the defocusing nonlinear Schrödinger equation. The two-phase solutions are explicitly parametrized in terms of two physically-meaningful variables: the energy density and the momentum density. Cavitation, viz., a minimum amplitude of zero, occurs if and only if the length of the largest spectral band is less than or equal to the sum of the lengths of the two smaller spectral bands. In the case of strict inequality, there are exactly two cavitation points in each period parallelogram.