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Journal of Mathematical Physics / Volume 27 / Issue 1

J. Math. Phys. 27, 14 (1986); http://dx.doi.org/10.1063/1.527381 (10 pages)

Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles

M. A. Del Olmo, M. A. Rodríguez, and P. Winternitz

Centre de recherches mathématiques, Université de Montréal, C. P. 6128, succ. A, Montréal, Québec, Canada H3C 3J7

(Received 3 May 1985; accepted 10 July 1985)

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 and PACS

Keywords

DIFFERENTIAL EQUATIONS, NONLINEAR PROBLEMS, LIE GROUPS, SL GROUPS, O GROUPS, ANALYTICAL SOLUTION, RICCATI EQUATION, VECTOR FIELDS, SP GROUPS, MATRICES, SINGULARITY, FIELD THEORIES

PACS

  • 02.30.Hq

    Ordinary differential equations

  • 11.10.Lm

    Nonlinear or nonlocal theories and models

  • 11.30.Na

    Nonlinear and dynamical symmetries (spectrum-generating symmetries)

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.527381

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    J. Harnad, P. Winternitz, and R. L. Anderson, J. Math. Phys. 24, 1062 (1983JMAPAQ000024000005001062000001).

    D. Ž. Djoković, J. Patera, P. Winternitz, and H. Zassenhaus, J. Math. Phys. 24, 1363 (1983JMAPAQ000024000006001363000001).

    M. J. Ablowitz, A. Ramani, and H. Segur, J. Math. Phys. 21, 715, 1006 (1980JMAPAQ000021000004000715000001).


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