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**Second order reductions of \(N\)-wave interactions related to low-rank simple Lie algebras.**
*(English)*
Zbl 0999.35037

Mladenov, I. M. (ed.) et al., Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, September 1-10, 1999. Sofia: Coral Press Scientific Publishing. 55-77 (2000).

Summary: We study the propagation of monochromatic fields in a layered medium. The mathematical model is derived from Maxwell’s equations. It consists of a nonlinear eigenvalue problem on the real axis with coefficients depending on the various layers.

A systematic analysis is carried out to uncover the various mechanisms leading to the bifurcation of asymmetric solutions even in a completely symmetric setting. We derive two particular simple conditions for the occurence of asymmetric bifurcation from the symmetric branch. One of these conditions occurs at a matching of the refractive indices across the interface while the other corresponds to a switching of the peak from the core to the cladding.

The rich bifurcation structure is illustrated by numerical calculations. Further stability considerations are included.

For the entire collection see [Zbl 0940.00039].

A systematic analysis is carried out to uncover the various mechanisms leading to the bifurcation of asymmetric solutions even in a completely symmetric setting. We derive two particular simple conditions for the occurence of asymmetric bifurcation from the symmetric branch. One of these conditions occurs at a matching of the refractive indices across the interface while the other corresponds to a switching of the peak from the core to the cladding.

The rich bifurcation structure is illustrated by numerical calculations. Further stability considerations are included.

For the entire collection see [Zbl 0940.00039].

### MSC:

35K15 | Initial value problems for second-order parabolic equations |

37K30 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures |

17B80 | Applications of Lie algebras and superalgebras to integrable systems |

78A60 | Lasers, masers, optical bistability, nonlinear optics |