Abstract
Semiclassically concentrated states of the nonlinear Schrödinger equation (NLSE) with unitary nonlinearity, representing multidimensional localized wave packets, are constructed on the basis of the Maslov complex germ theory. A system of ordinary differential equations of Hamilton-Ehrenfest (HE) type, describing the motion of the wave packet centroid, is derived. The structure of the HE system is strongly influenced by the initial conditions of the Cauchy problem for the NLSE. Wave packets of Gaussian type are constructed in an explicit form. Possible use of the solutions constructed in the problem of optical pulse propagation in a nonlinear medium with nonstationary dispersion is discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 598-606 |
| Number of pages | 9 |
| Journal | Russian Physics Journal |
| Volume | 42 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 1 Jan 1999 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Semiclassical trajectory-coherent states of the nonlinear Schrödinger equation with unitary nonlinearity. / Zhdaneev, O. V.; Sheehan, G. N.; Trifonov, A. Yu; Shapovalov, Aleksandr Vasilievich.
In: Russian Physics Journal, Vol. 42, No. 7, 01.01.1999, p. 598-606.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Semiclassical trajectory-coherent states of the nonlinear Schrödinger equation with unitary nonlinearity
AU - Zhdaneev, O. V.
AU - Sheehan, G. N.
AU - Trifonov, A. Yu
AU - Shapovalov, Aleksandr Vasilievich
PY - 1999/1/1
Y1 - 1999/1/1
N2 - Semiclassically concentrated states of the nonlinear Schrödinger equation (NLSE) with unitary nonlinearity, representing multidimensional localized wave packets, are constructed on the basis of the Maslov complex germ theory. A system of ordinary differential equations of Hamilton-Ehrenfest (HE) type, describing the motion of the wave packet centroid, is derived. The structure of the HE system is strongly influenced by the initial conditions of the Cauchy problem for the NLSE. Wave packets of Gaussian type are constructed in an explicit form. Possible use of the solutions constructed in the problem of optical pulse propagation in a nonlinear medium with nonstationary dispersion is discussed.
AB - Semiclassically concentrated states of the nonlinear Schrödinger equation (NLSE) with unitary nonlinearity, representing multidimensional localized wave packets, are constructed on the basis of the Maslov complex germ theory. A system of ordinary differential equations of Hamilton-Ehrenfest (HE) type, describing the motion of the wave packet centroid, is derived. The structure of the HE system is strongly influenced by the initial conditions of the Cauchy problem for the NLSE. Wave packets of Gaussian type are constructed in an explicit form. Possible use of the solutions constructed in the problem of optical pulse propagation in a nonlinear medium with nonstationary dispersion is discussed.
UR - http://www.scopus.com/inward/record.url?scp=17844394271&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=17844394271&partnerID=8YFLogxK
U2 - 10.1007/BF02513223
DO - 10.1007/BF02513223
M3 - Article
VL - 42
SP - 598
EP - 606
JO - Russian Physics Journal
JF - Russian Physics Journal
SN - 1064-8887
IS - 7
ER -