Title
On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrodinger equation
Abbreviated Journal Title
Commun. Pure Appl. Math.
Keywords
KORTEWEG-DEVRIES EQUATION; VARYING EXPONENTIAL WEIGHTS; SHABAT; EIGENVALUE PROBLEM; ASYMPTOTICS; POLYNOMIALS; RESPECT; GENERATION; POTENTIALS; Mathematics, Applied; Mathematics
Abstract
We calculate the leading-order term of the solution of the focusing nonlinear (cubic) Schrodinger 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 greater than or equal to 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. (C) 2004 Wiley Periodicals, Inc.
Journal Title
Communications on Pure and Applied Mathematics
Volume
57
Issue/Number
7
Publication Date
1-1-2004
Document Type
Article
DOI Link
Language
English
First Page
877
Last Page
985
WOS Identifier
ISSN
0010-3640
Recommended Citation
"On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrodinger equation" (2004). Faculty Bibliography 2000s. 4837.
https://stars.library.ucf.edu/facultybib2000/4837
Comments
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