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