On the non-integrability of the spherically-symmetric nonlinear Schrodinger equation in the Langmuir collapse problem

Citation
Bk. Shivamoggi et Dk. Rollins, On the non-integrability of the spherically-symmetric nonlinear Schrodinger equation in the Langmuir collapse problem, PHYS LETT A, 250(4-6), 1998, pp. 328-336
Citations number
15
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
PHYSICS LETTERS A
ISSN journal
0375-9601 → ACNP
Volume
250
Issue
4-6
Year of publication
1998
Pages
328 - 336
Database
ISI
SICI code
0375-9601(199812)250:4-6<328:OTNOTS>2.0.ZU;2-3
Abstract
In the present paper we give some analytic considerations of the sphericall y-symmetric nonlinear Schrodinger equation arising in the Langmuir collapse problem. We will make a systematic exploration of the various group symmet ries of this equation and show that the latter possesses only a three-param eter symmetry group. We will then give a variational formulation of this eq uation and use the three-parameter symmetry group to show that the equation in question possesses apparently only two polynomial conservation laws. Fi nally, we will make a study of the singularity structure of the present equ ation and show that it does not seem to possess the Painleve property. The conclusion is that the spherically-symmetric nonlinear Schrodinger equation in question is apparently not integrable. (C) 1998 Elsevier Science B.V.