Geometric Phases , Reduction and Lie-Poisson Structure for the Resonant Three-wave Interaction ∗

  title={Geometric Phases , Reduction and Lie-Poisson Structure for the Resonant Three-wave Interaction ∗},
  author={Mark S. Alber and Gregory G. Luther and J. M. Robbins},
Hamiltonian Lie-Poisson structures of the three-wave equations associated with the Lie algebras 5u(3) and 5u(2, 1) are derived and shown to be compatible. Poisson reduction is performed using the method of invariants and geometric phases associated with the reconstruction are calculated. These results can be applied to applications of nonlinear-waves in, for instance, nonlinear optics. Some of the general structures presented in the latter part of this paper are implicit in the literature; our… CONTINUE READING

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