99-221 B. Grebert, T. Kappeler
Symmetries of the Nonlinear Schr\"odinger Equation (53K, Latex) Jun 7, 99
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Abstract. Fundamental symmetries of the defocusing nonlinear Schr\"odinger equation are expressed in action-angle coordinates and characterized in terms of periodic and Dirichlet spectrum of the associated Zakharov-Shabat system. As a main application we prove a conjecture, raised by several experts in field, that the periodic spectrum is symmetric iff the sequence of gap lengths $(\gamma_k)_{k\in \mathbb {Z}}$ or, equivalently, the sequence of actions $(I_k)_{k\in \mathbb {Z}}$ is symmetric with respect to $k=0$.

Files: 99-221.src( 99-221.keywords , sym99.tex )