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