Open Access
September 2006 Instability of variable media to long waves with odd dispersion relations
Daniel Hodyss, Terrence R. Nathan
Commun. Math. Sci. 4(3): 669-676 (September 2006).


The instability of variable media to a broad class of long waves having dispersion relations that are an odd function of wavenumber is examined. For Hamiltonian media, new necessary conditions for the existence and structure of global modes are obtained. For non-Hamiltonian media, an analysis of the complex WKB branch points yields explicit expressions for the frequency and structure of the global modes, which manifest as spatially oscillatory wave packets or smooth envelope structures. These distinct modes and their locations within the media can be predicted by simply examining the local convergence or divergence of the group velocity in the long wave limit.


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Daniel Hodyss. Terrence R. Nathan. "Instability of variable media to long waves with odd dispersion relations." Commun. Math. Sci. 4 (3) 669 - 676, September 2006.


Published: September 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1115.76031
MathSciNet: MR2247936

Primary: 76E09
Secondary: 37K45 , 76E15

Keywords: Hamiltonian dynamics , Linear instability , long waves , variable media

Rights: Copyright © 2006 International Press of Boston

Vol.4 • No. 3 • September 2006
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