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- W2070613595 abstract "In a previous paper we considered numerically travelling wave solutions of the Kuramoto-Sivashinsky equation, and found solutions in each of three categories, these being regular shocks, oscillatory shocks and solitary waves. Here we show that there are no regular shocks when a certain parameter, representing the effect of short-wave stability, is asymptotically small, even though an asymptotic expansion in this parameter appears to establish at least asymptotic existence. The explanation is because of the presence of a term exponentially small in this parameter. The calculation of this term requires “asymptotics beyond all orders” and our calculation is based on a method used by Kruskal and Segur for a related propblem." @default.
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- W2070613595 date "1991-06-01" @default.
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- W2070613595 title "The non-existence of a certain class of travelling wave solutions of the Kuramoto-Sivashinsky equation" @default.
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- W2070613595 doi "https://doi.org/10.1016/0167-2789(91)90177-b" @default.
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