Instabilities of Multihump Vector Solitons in Coupled Nonlinear Schrödinger Equations

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.