D.E. Pelinovsky and J. Yang

Instabilities of multi-hump vector solitons in coupled nonlinear Schrodinger equations

Studies in Applied Mathematics 115, 109-137 (2005)

Abstract:
Spectral stability of multi-hump vector solitons in the Hamiltonian system of coupled nonlinear Schr\"{o}dinger (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. We also determine the eigenvalue spectrum numerically by the shooting method. The analysis is applied to two systems of coupled NLS equations with cubic and saturable nonlinearities. In the former case, we found that all multi-hump vector solitons in the non-integrable model are linearly unstable. In the latter case, stable multi-hump vector solitons are found in certain parameter regions, and some errors in the literature are corrected.

Keywords:
COUPLED NONLINEAR SCHRODINGER EQUATIONS, SOLITARY WAVES, SPECTRAL STABILITY, LINEARIZED HAMILTONIANS, CUBIC AND SATURABLE NONLINEARITIES, UNSTABLE EIGENVALUES