Finite mode analysis of the generalized Kuramoto-Sivashinsky equation

We present numerical results concerning a five mode truncation of the equation u t + uu x + δu xxx + u xx + u xxxx = 0 subject to periodic boundary conditions. We find that for large δ the system evolves from most initial conditions into a final state consisting of one or two traveling pulses, depen...

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Bibliographic Details
Published in:Physica. D 1992-12, Vol.61 (1), p.1-5
Main Authors: Alfaro, C.M., Benguria, R.D., Depassier, M.C.
Format: Article
Language:English
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Summary:We present numerical results concerning a five mode truncation of the equation u t + uu x + δu xxx + u xx + u xxxx = 0 subject to periodic boundary conditions. We find that for large δ the system evolves from most initial conditions into a final state consisting of one or two traveling pulses, depending on the initial condition and horizontal periodicity. This is due to a region of simultaneous stability of the first two branches that bifurcate from the trivial solution. An additional two pulse traveling wave which does not bifurcate from u = 0 is also present.
ISSN:0167-2789
1872-8022
DOI:10.1016/0167-2789(92)90143-B