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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2145-2155 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Superposition formulas are derived expressing the general solution of several different systems of nonlinear ordinary differential equations in terms of a fundamental set of particular solutions. The equations, as well as the superposition formulas, are induced by the action of the exceptional Lie group G2 (complex or real) on a homogeneous space G2/G, where G⊆G2 is a maximal subgroup of G2. When G is either parabolic, or simple, three particular solutions are needed. When G is SL(2,C)×SL(2,C) (or one of its real forms), then two particular solutions suffice.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2528-2534 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Nonlinear superequations, for which the general solution can be expressed algebraically in terms of a finite number of particular solutions, are obtained. They are based on the orthosymplectic supergroup OSP(m,2n) and its action on a homogeneous superspace. Superposition formulas are discussed for the cases m=1, n arbitrary, and m=2, n=1. For OSP(2,2) the number of particular solutions needed to reconstruct the general solution depends on the dimension of the underlying Grassmann algebra, whereas for OSP(1,2n) it does not.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Physics Letters A 118 (1986), S. 319-321 
    ISSN: 0375-9601
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Annals of Physics 231 (1994), S. 211-233 
    ISSN: 0003-4916
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 1072-1076 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Conformal space-time symmetries of electromagnetic fields and potentials are studied in order to determine whole sets of constants of motion when spin- 1/2 charged particles interact with such external electromagnetic fields. The relativistic and nonrelativistic contexts are discussed through the Hamiltonian formalism. In particular, the interesting example of the magnetic monopole field is recovered and related to the recent works of Jackiw and D'Hoker–Vinet.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2217-2227 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In order to study nonlinear ordinary differential equations with superposition principles, related to the exceptional simple Lie group G2, the complex and real forms of its Lie algebra are examined and their maximal subalgebras are summarized. In particular the parabolic subalgebras of the noncompact real form gNC2(R) are determined. Explicit matrix realizations of the fundamental representation D(1,0) are used and studied in connection with invariant subspaces in a seven-dimensional (complex or real) vector space. The results are collected in three tables of specific interest for the study of nonlinear differential equations, which will be developed in Paper II of this series.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 477-484 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The general formalism of N=2 pseudomechanics in the superspace is presented for one spatial dimension. Taking into account the (super) symmetries of the Lagrangian, an exhaustive classification of superpotentials into three categories is obtained. The first class contains the harmonic oscillator potential, the free particle constant potential, and the superposition of both with a linear potential. The second one contains the λ2/q2 potential and its superposition with the harmonic oscillator potential and a constant one. The third class contains all other potentials. Through Noether's theorem, conserved quantities are associated with (super)symmetry properties, and, for each class, we, respectively, get the following superalgebras: osp(2,2) (D'Alembertian) sh(1), osp(2,2), and spl(1,1) (D'Alembertian) so(2).
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 925-928 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Harnad–Shnider–Vinet study of symmetry properties on gauge fields in terms of invariant connections on principal fiber bundles is reviewed in the simple U(1)-gauge theory. It is extended to the case of invariant electromagnetic fields admitting nontrivial extensions of their symmetry groups. Some specific examples are discussed.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 520-529 
    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
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1951-1965 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The method of symmetry reduction is used to solve Grassmann-valued differential equations. The (N=2) supersymmetric Korteweg–de Vries equation is considered. It admits a Lie superalgebra of symmetries of dimension 5. A two-dimensional subsuperalgebra is chosen to reduce the number of independent variables in this equation. We are then able to give different types of exact solutions, in particular soliton solutions. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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