Nonlinear Superposition Formulas Based on Lie Group SO(n+1,n)

2000/08/17 by C. Burdik, Burdik, C., O. Navratil +1
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0008019

11 pages, LaTeX

arxiv created 2000/08/17 · arxiv updated 2009/11/30

Abstract

Systems of nonlinear ordinary differential equations are constructed, for which the general solution is algebraically expressed in terms of a finite number of particular solutions. Expressions of that type are called the nonlinear superposition formulas. These systems are connected with local Lie groups tranformations on their homogeneous spaces. In the presented work the nonlinear superposition formulas are constructed for the case of the SO(3,2) group and some aspects in the general case of SO(n+1,n) are studied.

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