Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles
- 1 January 1986
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 27 (1) , 14-23
- https://doi.org/10.1063/1.527381
Abstract
Nonlinear ordinary differential equations admitting a superposition principle based on the action of the group SL(n,C) on the homogeneous spaces SL(n,C)/O(n,C) and SL(n,C)/Sp(n,C) are derived. The superposition formulas are presented explicitly. In the O(n,C) case the general solution is expressed in terms of three particular solutions (for any n). For the Sp(n,C) case three solutions are needed for n=2k≥8, four solutions for n=6, and five solutions for n=4.Keywords
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