ASYMPTOTIC-BEHAVIOR OF THE SELF-DEFOCUSING NONLINEAR SCHRODINGER-EQUATION FOR PIECEWISE-CONSTANT INITIAL CONDITIONS

In this paper we use a transfer matrix method to calculate the asympto tic behavior of the nonlinear Schrodinger (NLS) equation in a self-def ocusing medium for piecewise constant initial conditions. Treating ini tial conditions that consist of m repeated regions, we show that the e igenvalues associated with this problem appear in bands, and, as m ten ds to infinity, we obtain the eigenvalue density of states for these b ands. Comparing results from the transfer matrix approach to the resul ts for a Bloch function method, we show that the edges of a region wit h periodic initial conditions result in a finite number of additional eigenvalues that appear outside the bands.