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 and Dmitry Pelinovsky
Where published*	SIAM J. Appl. Dyn. Syst.
How published*	Journal
Year*	2005
Volume	5
Number	-1
Pages	66-83
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Abstract	We consider the Hamiltonian first-order 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 fast numerical computations of eigenvalues with the Chebyshev interpolation algorithm.