2005/06/17 by Jianke Yang, Yang, Jianke
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Numerical methods for differential equations #Pattern Formation and Solitons (nlin.PS) #nlin.PS
paper · pdf · doi:10.48550/arxiv.nlin/0506036
To appear in AMS book series 'Contemporary Mathematics' (2005)
arxiv created 2005/06/17 · openalex publication_date 2005/06/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Linear stability of multi-vector-soliton bound states in the coupled nonlinear Schrödinger equations is analyzed using a new tail-matching method. Under the condition that individual vector solitons in the bound states are wave-and-daughter-waves and widely separated, small eigenvalues of these bound states that bifurcate from the zero eigenvalue of single vector solitons are calculated explicitly. It is found that unstable eigenvalues from phase-mode bifurcations always exist, thus the bound states are always linearly unstable. This tail-matching method is simple, but it gives identical results as the Karpman-Solev'ev-Gorshkov-Ostrovsky method.