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  • 1
    Digitale Medien
    Digitale Medien
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 7109-7127 
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: We construct the general solutions of the system of nonlinear differential equations (D'Alembertian)nu=0, uμuμ=0 in the four- and five-dimensional complex pseudo-Euclidean spaces. The results obtained are used to reduce the multidimensional nonlinear d'Alembert equation (D'Alembertian)4u=F(u) to ordinary differential equations and to construct its new exact solutions. © 1995 American Institute of Physics.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5944-5959 
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A new approach for the analysis of partial differential equations is developed which is characterized by a simultaneous use of higher and conditional symmetries. Higher symmetries of the Schrödinger equation with an arbitrary potential are investigated. Nonlinear determining equations for potentials are solved using reductions to Weierstrass, Painlevé, and Riccati forms. Algebraic properties of higher order symmetry operators are analyzed. Combinations of higher and conditional symmetries are used to generate families of exact solutions of linear and nonlinear Schrödinger equations. © 1997 American Institute of Physics.
    Materialart: Digitale Medien
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  • 3
    Digitale Medien
    Digitale Medien
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 5506-5521 
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: We suggest an effective approach to separation of variables in the Schrödinger equation with two space variables. Using it we classify inequivalent potentials V(x1,x2) such that the corresponding Schrödinger equations admit separation of variables. Besides that, we carry out separation of variables in the Schrödinger equation with the anisotropic harmonic oscillator potential V=k1x21+k2x22 and obtain a complete list of coordinate systems providing its separability. Most of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schrödinger equation (V=0). © 1995 American Institute of Physics.
    Materialart: Digitale Medien
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Communications in mathematical physics 212 (2000), S. 535-556 
    ISSN: 1432-0916
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract: We classify realizations of the Lie algebras of the rotation O(3) and Euclid E(3) groups within the class of first-order differential operators in arbitrary finite dimensions. It is established that there are only two distinct realizations of the Lie algebra of the group O(3) which are inequivalent within the action of a diffeomorphism group. Using this result we describe a special subclass of realizations of the Euclid algebra which are called covariant ones by analogy to similar objects considered in classical representation theory. Furthermore, we give an exhaustive description of realizations of the Lie algebra of the group O(4) and construct covariant realizations of the Lie algebra of the generalized Euclid group E(4).
    Materialart: Digitale Medien
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