Abstract
A numerical method to study radially symmetric standing wave solutions (with arbitrarily large number of nodes) to the nonlinear Schrödinger equation is described and used to study several new geometric features of these waves. The method is based on numerically locating the basin boundary (separating surface) between two attracting invariant lines in phase space. Each solution trajectory lies on the basin boundary, and is computed by ‘squeezing’ it between two adjacent asymptotically stable trajectories. Of particular interest is the asymptotic distribution of the eigenvalues and the conserved quantities, which follow power law behavior. Also of interest is the geometry of the basin boundary, which shows that the solution with a prescribed number of zeroes is unique.
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