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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 SIAM Journal on Applied Dynamical Systems, 4 (1). pp. 140-158. ISSN 15360040


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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 us to locate exactly where the unstable discrete eigenvalues detach from the continuous spectrum. Moreover, the algorithm allows for stable shooting along multidimensional 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 AUNSPECIFIED
Date : 1 January 2005
Identification Number : 10.1137/040605308
Additional Information : Published in <i>SIAM Journal on Applied Dynamical Systems,</i> Vol. 4, Iss. 1, pp. 140 - 158. Copyright 2005 Society for Industrial and Applied Mathematics. Click <a href=>here</a> to access the journal's website.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 23 Sep 2013 18:33

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