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Instabilities of Multihump Vector Solitons in Coupled Nonlinear Schrödinger Equations
Author(s) -
Pelinovsky Dmitry E.,
Yang Jianke
Publication year - 2005
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2005.01565
Subject(s) - eigenvalues and eigenvectors , nonlinear system , hamiltonian (control theory) , shooting method , hamiltonian system , mathematics , mathematical analysis , schrödinger equation , physics , mathematical physics , schrödinger's cat , classical mechanics , quantum mechanics , boundary value problem , mathematical optimization
Spectral stability of multihump vector solitons in the Hamiltonian system of coupled nonlinear Schrödinger (NLS) equations is investigated both analytically and numerically. Using the closure theorem for the negative index of the linearized Hamiltonian, we classify all possible bifurcations of unstable eigenvalues in the systems of coupled NLS equations with cubic and saturable nonlinearities. We also determine the eigenvalue spectrum numerically by the shooting method. In case of cubic nonlinearities, all multihump vector solitons in the nonintegrable model are found to be linearly unstable. In case of saturable nonlinearities, stable multihump vector solitons are found in certain parameter regions, and some errors in the literature are corrected.