Stability criterion for multi-component solitary waves

Details Stability criterion for multi-component solitary waves Stability criterion for multi-component solitary waves

2000-06-22

arxiv.org/abs/nlin/0006036v1

Nonlinear Sciences

Pattern Formation and Solitons

submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.62.8668

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.

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