A. Tovbis et S. Venakides, The eigenvalue problem for the focusing nonlinear Schrodinger equation: new solvable cases, PHYSICA D, 146(1-4), 2000, pp. 150-164
In this paper, we study the semi-classical limit of the Zakharov-Shabat eig
envalue problem for the focusing of NLS with some specific initial data. In
all these cases, the eigenvalue problem is reduced to connection problems
for the hypergeometric equation and for other classical equations. The spec
ial initial data [Suppl. Frog. Theor. Phys, 55 (1974) 284] is contained in
our family of initial data, parameterized by a real parameter mu, as a part
icular case mu = 0. We find that beyond a certain value of the parameter mu
, the pure-point spectrum becomes empty and all the scattering information
is contained in the reflection coefficient. (C) 2000 Published by Elsevier
Science B.V.