Title

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

Abstract

In the present paper we give some analytic considerations of the spherically-symmetric nonlinear Schrödinger equation arising in the Langmuir collapse problem. We will make a systematic exploration of the various group symmetries of this equation and show that the latter possesses only a three-parameter symmetry group. We will then give a variational formulation of this equation and use the three-parameter symmetry group to show that the equation in question possesses apparently only two polynomial conservation laws. Finally, we will make a study of the singularity structure of the present equation and show that it does not seem to possess the Painlevé property. The conclusion is that the spherically-symmetric nonlinear Schrödinger equation in question is apparently not integrable. © 1998 Elsevier Science B.V.

Publication Date

12-28-1998

Publication Title

Physics Letters, Section A: General, Atomic and Solid State Physics

Volume

250

Issue

4-6

Number of Pages

328-336

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0375-9601(98)00803-2

Socpus ID

0346399872 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0346399872

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