title: Stability analysis of embedded solitons in the generalized third-order nonlinear Schrodinger equation.
abstract: We study the generalized third-order nonlinear Schrodinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons.
authors.affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada.
authors.forename: Dmitry E
authors.initials: DE
authors.lastname: Pelinovsky
authors.forename: Jianke
authors.initials: J
authors.lastname: Yang
mesh_terms: D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D008954:Models, Biological; D017711:Nonlinear Dynamics