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.
| Original language | English |
|---|---|
| Pages (from-to) | 127-138 |
| Number of pages | 12 |
| Journal | Journal of Nonlinear Mathematical Physics |
| Volume | 6 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Jan 1999 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Semiclassical solutions of the nonlinear schrödinger equation. / Shapovalov, Aleksandr Vasilievich; Trifonov, A. Yu.
In: Journal of Nonlinear Mathematical Physics, Vol. 6, No. 2, 01.01.1999, p. 127-138.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Semiclassical solutions of the nonlinear schrödinger equation
AU - Shapovalov, Aleksandr Vasilievich
AU - Trifonov, A. Yu
PY - 1999/1/1
Y1 - 1999/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33947152569&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33947152569&partnerID=8YFLogxK
U2 - 10.2991/jnmp.1999.6.2.2
DO - 10.2991/jnmp.1999.6.2.2
M3 - Article
VL - 6
SP - 127
EP - 138
JO - Journal of Nonlinear Mathematical Physics
JF - Journal of Nonlinear Mathematical Physics
SN - 1402-9251
IS - 2
ER -