Biunitary transformations and ordinary differential equations.—II


We use the results of a recent reformulation of the theory of arbitrary-order differential equations in terms of non-Hermitian operators to show that the invariant binorm is associated to a generalized Courant-Snyder invariant. Furthermore, we indicate the existence of higher-order invariants associated to the Casimir operators of the group, utilized to treat higher-order equations. We also discuss the intrinsic supersymmetric nature of the theory developed. Finally, we show the relevance of the proposed mathematical technique to the design of fiberoptics transport systems.

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Dattoli, G., Loreto, V., Mari, C. et al. Biunitary transformations and ordinary differential equations.—II. Nuovo Cim B 106, 1375–1390 (1991).

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PACS 02.30.Hq

  • Ordinary differential equations

PACS 02.20.Tw

  • Infinite-dimensional Lie groups
  • PACS 42.10
  • Propagation and transmission in homogeneous media

PACS 41.80

  • Particle beams and particle optics