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Stability criterion for multi-component solitary waves

Dmitry E. Pelinovsky·Yuri S. Kivshar
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Abstract

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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Dmitry E. Pelinovsky, Yuri S. Kivshar. 2000-06-22. Stability criterion for multi-component solitary waves. https://doi.org/10.1103/physreve.62.8668

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