Block-diagonalization of the linearized coupled-mode system

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.

16 pages, 2 figuresn

References in corpus (2)

• Bifurcations and stability of gap solitons in periodic potentials
• A robust numerical method to study oscillatory instability of gap solitary waves

Cited by in corpus (21)

• Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices
• Numerical methods for nonlinear Dirac equation
• Dimer with gain and loss: Integrability and $\mathcal{P}\mathcal{T}$-symmetry restoration
• Orbital stability of Dirac solitons
• Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model
• Feshbach Resonance Management of Bose-Einstein Condensates in Optical Lattices
• Spinor solitons and their $\mathcal{P}\mathcal{T}$-symmetric offspring
• Global strong solution to a nonlinear Dirac type equation in one dimension
• Survey on global existence in the nonlinear Dirac equations in one dimension
• Moving gap solitons in periodic potentials
• Solitary waves in the Nonlinear Dirac Equation
• Transverse instability of line solitons in massive Dirac equations
• Asymptotic stability of small gap solitons in the nonlinear Dirac equations
• Symplectic transversality and the Pego-Weinstein theory
• Broad Band Solitons in a Periodic and Nonlinear Maxwell System
• On global attraction to quantum stationary states. Dirac equation with mean field interaction
• Stability of parametrically driven, damped nonlinear Dirac solitons
• Experimental evidence of percolation phase transition in surface plasmons generation
• Decay of solutions of nonlinear Dirac equations
• Results on the spectral stability of standing wave solutions of the Soler model in 1-D
• Families of solitons in Bragg supergratings