The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases
Journal Article (Journal Article)
In this paper, we study the semi-classical limit of the Zakharov-Shabat eigenvalue 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 special initial data [Suppl. Prog. Theor. Phys. 55 (1974) 284] is contained in our family of initial data, parameterized by a real parameter μ, as a particular case μ=0. We find that beyond a certain value of the parameter μ, the pure-point spectrum becomes empty and all the scattering information is contained in the reflection coefficient.
Full Text
Duke Authors
Cited Authors
- Tovbis, A; Venakides, S
Published Date
- November 15, 2000
Published In
Volume / Issue
- 146 / 1-4
Start / End Page
- 150 - 164
International Standard Serial Number (ISSN)
- 0167-2789
Digital Object Identifier (DOI)
- 10.1016/S0167-2789(00)00126-3
Citation Source
- Scopus