On the Stability of Periodic Solutions of Nonlinear Dispersive Equations
Johnson, Mathew A.
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https://hdl.handle.net/2142/86925
Description
Title
On the Stability of Periodic Solutions of Nonlinear Dispersive Equations
Author(s)
Johnson, Mathew A.
Issue Date
2009
Doctoral Committee Chair(s)
Bronski, Jared C.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
Finally, we show how our results extend to other classes of dispersive equations. In particular, we derive modulational and finite-wavelength instability indices for the generalized Benjamin-Bona-Mahony (gBBM) equation, as well as the generalized Camassa-Holm equation. Moreover, we prove a transverse instability result for the gBBM equation analogous to that for the gKdV.
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