Stability criterion for multicomponent solitary waves

Dmitry E. Pelinovsky and Yuri S. Kivshar
Phys. Rev. E 62, 8668 – Published 1 December 2000
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Abstract

We obtain the most general matrix criterion for stability and instability of multicomponent solitary waves by considering a system of N incoherently coupled nonlinear Schrödinger 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 multicomponent 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.

  • Received 22 June 2000

DOI:https://doi.org/10.1103/PhysRevE.62.8668

©2000 American Physical Society

Authors & Affiliations

Dmitry E. Pelinovsky* and Yuri S. Kivshar

  • Optical Sciences Centre, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, ACT 0200, Australia

  • *Permanent address: Department of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1. Email address: dmpeli@math.mcmaster.ca

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Vol. 62, Iss. 6 — December 2000

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