M. Chugunova and D. Pelinovsky

Block-diagonalization of the symmetric first-order coupled-mode system

SIAM Journal of Applied Dynamical Systems 5, 66-83 (2006)

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.

Hamiltonian first-order coupled-mode systems, gap solitons, spectral stability, invariant subspaces, eigenvalues