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Symmetries and Conditional Symmetries of a Non-relativistic Chern-Simons System

✍ Scribed by D. Levi; L. Vinet; P. Winternitz

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
589 KB
Volume
230
Category
Article
ISSN
0003-4916

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✦ Synopsis

The symmetry algebra of the planar nonlinear Schrödinger equation minimally coupled to Chern-Simons gauge fields is systematically determined. It is confirmed to be the semidirect sum of the eight dimensional Schrödinger algebra sch(2) (with no central extension) and of the infinitesimal gauge transformation algebra. The conditional symmetries that arise when self-duality is imposed are also discussed and found to have, as expected, a Kac-MoodyVirasoro structure. Several examples of symmetry reductions to ordinary differential equations are presented and non-self-dual solutions are obtained. The non-self-dual system is shown not to have the Painleve property. 1994 Academic Press. Inc

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