Abstract
A KdV equation modified by viscosity is derived for weakly nonlinear long waves propagating in a channel of uniform but arbitrary cross section. The case of high Reynolds number is considered, and the method of matched asymptotic expansion is employed. The equation derived here is found to be similar to the corresponding equation for a two-dimensional layer of liquid derived by previous authors. The only difference is that the dispersive, nonlinear, and viscous terms are multiplied by constants dependent on the cross section geometry of the channel.
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