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A robust numerical method to study oscillatory instability of gap solitary waves

Derks, Gianne and Gottwald, Georg A. (2005) A robust numerical method to study oscillatory instability of gap solitary waves Dynamical Systems, 4. pp. 140-158.


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The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to eigenvalues. These problems may exhibit oscillatory instabilities where eigenvalues detach from the edges of the continuous spectrum, so called edge bifurcations. A numerical framework, based on a fast robust shooting algorithm using exterior algebra is described. The complete algorithm is robust in the sense that it does not produce spurious unstable eigenvalues. The algorithm allows to locate exactly where the unstable discrete eigenvalues detach from the continuous spectrum. Moreover, the algorithm allows for stable shooting along multi-dimensional stable and unstable manifolds. The method is illustrated by computing the stability and instability of gap solitary waves of a coupled mode model.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Gottwald, Georg A.
Date : 22 February 2005
Uncontrolled Keywords : gap solitary wave, numerical Evans function, edge bifurcation, exterior algebra, oscillatory instability, massive Thirring model
Additional Information : First publihsed in the SIAM Journal on Applied Dynamical Systems, 4, 140-158. © 2005 Society for Industrial and Applied Mathematics.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 06 Jul 2019 05:07

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