ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Nonlinear equations with superposition formulas are obtained, corresponding to the action of the complex and real forms of the exceptional Lie group G2 on the homogeneous spaces G2/H. The isotropy group of the origin H is taken as one of the maximal parabolic subgroups of G2, or as one of the maximal reductive subgroups, leaving some vector space V∈C7 (or V∈R7) invariant. The parabolic subgroups, as well as the simple subgroups SL(3,C), SU(3), SL(3,R) or SU(2,1) lead to equations with quadratic or quartic nonlinearities. The semisimple subgroups SL(2,C)⊗SL(2,C), SU(2)⊗SU(2), and SU(1,1)⊗SU(1,1) lead to equations with quadratic nonlinearities and additional nonlinear constraints on the independent variables.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527636
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