On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation
Publication
, Journal Article
Tovbis, A; Venakides, S; Zhou, X
Published in: Communications on Pure and Applied Mathematics
July 1, 2004
We calculate the leading-order term of the solution of the focusing nonlinear (cubic) Schrödinger equation (NLS) in the semiclassical limit for a certain one-parameter family of initial conditions. This family contains both solitons and pure radiation. In the pure radiation case, our result is valid for all times t ≥ 0. We utilize the Riemann-Hilbert problem formulation of the inverse scattering problem to obtain the leading-order term of the solution. Error estimates are provided. © 2004 Wiley Periodicals, Inc.
Duke Scholars
Published In
Communications on Pure and Applied Mathematics
DOI
ISSN
0010-3640
Publication Date
July 1, 2004
Volume
57
Issue
7
Start / End Page
877 / 985
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Tovbis, A., Venakides, S., & Zhou, X. (2004). On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation. Communications on Pure and Applied Mathematics, 57(7), 877–985. https://doi.org/10.1002/cpa.20024
Tovbis, A., S. Venakides, and X. Zhou. “On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation.” Communications on Pure and Applied Mathematics 57, no. 7 (July 1, 2004): 877–985. https://doi.org/10.1002/cpa.20024.
Tovbis A, Venakides S, Zhou X. On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation. Communications on Pure and Applied Mathematics. 2004 Jul 1;57(7):877–985.
Tovbis, A., et al. “On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation.” Communications on Pure and Applied Mathematics, vol. 57, no. 7, July 2004, pp. 877–985. Scopus, doi:10.1002/cpa.20024.
Tovbis A, Venakides S, Zhou X. On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation. Communications on Pure and Applied Mathematics. 2004 Jul 1;57(7):877–985.
Published In
Communications on Pure and Applied Mathematics
DOI
ISSN
0010-3640
Publication Date
July 1, 2004
Volume
57
Issue
7
Start / End Page
877 / 985
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics