Journal of Nonlinear Mathematical Physics

Volume 6, Issue 2, May 1999, Pages 127 - 138

Semiclassical Solutions of the Nonlinear Schrödinger Equation

Authors
A.V. SHAPOVALOV, A.Yu. TRIFONOV
Corresponding Author
A.V. SHAPOVALOV
Available Online 1 May 1999.
DOI
https://doi.org/10.2991/jnmp.1999.6.2.2How to use a DOI?
Abstract
A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schrödinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass of such a solution is shown to move along with the bicharacteristics of the basic symbol of the corresponding linear Schrödinger equation. The leading term of the asymptotic WKBsolution is constructed for the multidimensional NLSE. Special cases are considered for the standard one-dimensional NLSE and for NLSE in cylindrical coordinates.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
6 - 2
Pages
127 - 138
Publication Date
1999/05
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1999.6.2.2How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - A.V. SHAPOVALOV
AU  - A.Yu. TRIFONOV
PY  - 1999
DA  - 1999/05
TI  - Semiclassical Solutions of the Nonlinear Schrödinger Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 127
EP  - 138
VL  - 6
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1999.6.2.2
DO  - https://doi.org/10.2991/jnmp.1999.6.2.2
ID  - SHAPOVALOV1999
ER  -