Title
The eigenvalue problem for the focusing nonlinear Schrodinger equation: new solvable cases
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
ISSN
0167-2789
Recommended Citation
"The eigenvalue problem for the focusing nonlinear Schrodinger equation: new solvable cases" (2000). Faculty Bibliography 2000s. 2830.
https://stars.library.ucf.edu/facultybib2000/2830
Comments
Authors: contact us about adding a copy of your work at STARS@ucf.edu