Title

The Eigenvalue Problem For The Focusing Nonlinear Schrödinger Equation: New Solvable Cases

Keywords

Focusing nonlinear Schrödinger equation; Hypergeometric functions; Semi-classical limit; Zakharov-Shabat eigenvalue problem

Abstract

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.

Publication Date

11-15-2000

Publication Title

Physica D: Nonlinear Phenomena

Volume

146

Issue

1-4

Number of Pages

150-164

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0167-2789(00)00126-3

Socpus ID

0039741902 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0039741902

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