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Math and StatisticsNumerical Mathematics

Modulational Stability of Periodic Solutions of the Kuramoto-Sivashinsky Equation

Authors: Demetrios T. Papageorgiou; George C. Papanicolaou; Yiorgos S. Smyrlis; INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
Abstract:
We study the long-wave, modulational, stability of steady periodic solutions of the Kuramoto-Sivashinsky equation. The analysis is fully nonlinear at first, and can in principle be carried out to all orders in the small parameter, which is the ratio of the spatial period to a characteristic length of the envelope perturbations. In the linearized regime we recover a high-order version of the results of Frisch, She and Thual, which shows that the periodic waves are much more stable than previously expected. Modulation theory, Nonlinear stability

Description: Contractor rept.
Pages: 30
Report Date: JUL 93
Contract Number: NAS1-18605, NAS1-19480
Report Number: A821962

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Keywords relating to this report:
*Modulation
*NONLINEAR DIFFERENTIAL EQUATIONS
LENGTH
PARAMETERS
PERTURBATIONS
RATIOS
STABILITY
THEORY
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