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. Keywords: