Title

The eigenvalue problem for the focusing nonlinear Schrodinger equation: new solvable cases

Authors

Authors

A. Tovbis;S. Venakides

Comments

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Abbreviated Journal Title

Physica D

Keywords

Zakharov-Shabat eigenvalue problem; semi-classical limit; focusing; nonlinear Schrodinger equation; hypergeometric functions; Mathematics, Applied; Physics, Multidisciplinary; Physics, Mathematical

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. Frog. Theor. Phys, 55 (1974) 284] is contained in our family of initial data, parameterized by a real parameter mu, as a particular 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.

Journal Title

Physica D

Volume

146

Issue/Number

1-4

Publication Date

1-1-2000

Document Type

Article

Language

English

First Page

150

Last Page

164

WOS Identifier

WOS:000165117000005

ISSN

0167-2789

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