The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases
Publication
, Journal Article
Tovbis, A; Venakides, S
Published in: Physica D: Nonlinear Phenomena
November 15, 2000
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.
Duke Scholars
Published In
Physica D: Nonlinear Phenomena
DOI
ISSN
0167-2789
Publication Date
November 15, 2000
Volume
146
Issue
1-4
Start / End Page
150 / 164
Related Subject Headings
- Fluids & Plasmas
- 4903 Numerical and computational mathematics
- 4902 Mathematical physics
- 4901 Applied mathematics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Tovbis, A., & Venakides, S. (2000). The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases. Physica D: Nonlinear Phenomena, 146(1–4), 150–164. https://doi.org/10.1016/S0167-2789(00)00126-3
Tovbis, A., and S. Venakides. “The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases.” Physica D: Nonlinear Phenomena 146, no. 1–4 (November 15, 2000): 150–64. https://doi.org/10.1016/S0167-2789(00)00126-3.
Tovbis A, Venakides S. The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases. Physica D: Nonlinear Phenomena. 2000 Nov 15;146(1–4):150–64.
Tovbis, A., and S. Venakides. “The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases.” Physica D: Nonlinear Phenomena, vol. 146, no. 1–4, Nov. 2000, pp. 150–64. Scopus, doi:10.1016/S0167-2789(00)00126-3.
Tovbis A, Venakides S. The eigenvalue problem for the focusing nonlinear Schrödinger equation: New solvable cases. Physica D: Nonlinear Phenomena. 2000 Nov 15;146(1–4):150–164.
Published In
Physica D: Nonlinear Phenomena
DOI
ISSN
0167-2789
Publication Date
November 15, 2000
Volume
146
Issue
1-4
Start / End Page
150 / 164
Related Subject Headings
- Fluids & Plasmas
- 4903 Numerical and computational mathematics
- 4902 Mathematical physics
- 4901 Applied mathematics
- 0102 Applied Mathematics