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
Received 7 November 1998, Accepted 20 January 1999, Available Online 1 May 1999.
- DOI
- 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.
- Copyright
- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - A.V. Shapovalov AU - A.Yu. Trifonov PY - 1999 DA - 1999/05/01 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 - 10.2991/jnmp.1999.6.2.2 ID - Shapovalov1999 ER -