D.E. Pelinovsky and Yu.S. Kivshar
Stability criterion for multi-component solitary waves
Phys. Rev. E 62, 8668-8676 (2000)
We obtain the most general matrix criterion for stability and
instability of multi-component solitary waves considering a
system of N incoherently coupled nonlinear Schrodinger equations.
Soliton stability is studied as a constrained variational
problem which is reduced to finite-dimensional linear algebra.
We prove that unstable (all real and positive) eigenvalues of
the linear stability problem for multi-component solitary waves
are connected with negative eigenvalues of the Hessian matrix,
the latter is constructed for the energetic surface of
N-component spatially localized stationary solutions.