English

Block-diagonalization of the linearized coupled-mode system

Dynamical Systems 2009-11-11 v1 Numerical Analysis

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 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.

Keywords

Cite

@article{arxiv.math/0504442,
  title  = {Block-diagonalization of the linearized coupled-mode system},
  author = {M. Chugunova and D. Pelinovsky},
  journal= {arXiv preprint arXiv:math/0504442},
  year   = {2009}
}

Comments

16 pages, 2 figuresn