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Zbl 0977.35123
Schneider, Guido; Wayne, C.Eugene
Kawahara dynamics in dispersive media. (English)
[J] Physica D 152-153, 384-394 (2001). ISSN 0167-2789

Summary: In a previous paper it was shown that in the long wave limit the water wave problem without surface tension can be described approximately by two decoupled KdV equations. Here, we study a model problem and prove that in a degenerate case which occurs for the water wave problem with surface tension and near other codimension two points at which the coefficient in front of the leading order dispersive term in the equation of motion vanishes, the long wave limit can be rigorously approximated by two decoupled Kawahara equations.

MSC 2000:: *35Q53 KdV-like equations
76B15 Wave motions (fluid mechanics)

Keywords: Kawahara equations; water wave problem; Boussines equation; long wave limit

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Zentralblatt MATH Berlin [Germany]