Block-diagonalization of the linearized coupled-mode system

Details Block-diagonalization of the linearized coupled-mode system Block-diagonalization of the linearized coupled-mode system

2005-04-21

arxiv.org/abs/math/0504442v1

Mathematics

Dynamical Systems

16 pages, 2 figuresn

Scientific paper

10.1137/050629781

We consider the Hamiltonian coupled-mode system that occur in nonlinear optics, photonics, and atomic physics. Spectral stability of gap solitons is determined by eigenvalues of the linearized coupled-mode system, which is equivalent to a four-by-four Dirac system with sign-indefinite metric. In the special class of symmetric nonlinear potentials, we construct a block-diagonal representation of the linearized equations, when the spectral problem reduces to two coupled two-by-two Dirac systems. The block-diagonalization is used in numerical computations of eigenvalues that determine stability of gap solitons.

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