NDLI: A Robust Numerical Method to Study Oscillatory Instability of Gap Solitary Waves

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A Robust Numerical Method to Study Oscillatory Instability of Gap Solitary Waves

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Derks, Gianne Gottwald, Georg A.
Copyright Year	2005
Abstract	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.
Starting Page	140
Ending Page	158
Page Count	19
File Format	PDF
DOI	10.1137/040605308
e-ISSN	15360040
Issue Number	1
Volume Number	4
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-07
Access Restriction	Subscribed
Subject Keyword	gap solitary wave Computational methods for bifurcation problems Bifurcation problems numerical Evans function oscillatory instability massive Thirring model edge bifurcation exterior algebra Nonlinear stabilities Solitary waves
Content Type	Text
Resource Type	Article

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