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Generalizations of the Toda molecule

Author

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  • Van Velthoven, W.P.G.
  • Bais, F.A.

Abstract

Finite-energy monopole solutions are constructed for the self-dual equations with spherical symmetry in an arbitrary integer graded Lie algebra. The constraint of spherical symmetry in a complex noncoordinate basis leads to a dimensional reduction. The resulting two-dimensional (r, t) equations are of second order and furnish new generalizations of the Toda molecule equations. These are then solved by a technique which is due to Leznov and Saveliev. For time-independent solutions a further reduction is made, leading to an ansatz for all SU(2) embeddings of the Lie algebra. The regularity condition at the origin for the solutions, needed to ensure finite energy, is also solved for a special class of nonmaximal embeddings. Explicit solutions are given for the groups SU(2), SO(4), Sp(4) and SU(4).

Suggested Citation

  • Van Velthoven, W.P.G. & Bais, F.A., 1986. "Generalizations of the Toda molecule," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 139(2), pages 326-358.
  • Handle: RePEc:eee:phsmap:v:139:y:1986:i:2:p:326-358
    DOI: 10.1016/0378-4371(86)90125-1
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    Cited by:

    1. Nieuwenhuizen, Th.M., 1989. "Dynamical properties of 2D systems with site disorder," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(3), pages 1101-1138.

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