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Complex parabolic subgroups of G 2 and nonlinear differential equations

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Abstract

Nonlinear ordinary differential equations with superposition formulas corresponding to the exceptional Lie group G 2ℂ and its two maximal (complex) parabolic subgroups are determined. The G 2-invariance of a third-order skewsymmetric tensor is exploited. The obtained ODEs have polynomial nonlinearities of order 2 in one case and of order 4 in the other.

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Authors and Affiliations

  1. Physique théorique et mathématique, Université de Liège, Institut de Physique au Sart Tilman, B. 5, B-4000, Liège 1, Belgium

    J. Beckers & V. Hussin

  2. Centre de Recherches Mathématiques, Université de Montréal, Succ. A, CP 6128, H3C 3J7, Montréal, Québec, Canada

    P. Winternitz

Authors
  1. J. Beckers
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  2. V. Hussin
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  3. P. Winternitz
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Additional information

Supported in part by ‘Les accords culturels Québec-Belgique 1985’.

Chargé de recherches FNRS.

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Beckers, J., Hussin, V. & Winternitz, P. Complex parabolic subgroups of G 2 and nonlinear differential equations. Lett Math Phys 11, 81–86 (1986). https://doi.org/10.1007/BF00417468

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  • DOI: https://doi.org/10.1007/BF00417468

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