Publication: Block-diagonalization of the symmetric first-order coupled-mode system.

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Title	Block-diagonalization of the symmetric first-order coupled-mode system.
Authors/Editors*	Marina Chugunova, Dmitry Pelinovsky
Where published*	SIAM Journal of Applied Dynamical Systems
How published*	Journal
Year*	2005
Volume	5
Number	-1
Pages	66-83
Publisher
Keywords	Hamiltonian coupled-mode systems, gap solitons, spectral stability, invariant subspaces, eigenvalues
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Abstract	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 equations, which are 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 coupled-mode 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.