Nonlinear PDE Phenomena

Abstract

In Section 3.2.1 the reader encountered the Korteweg–deVries (KdV) equation which has been successfully used to describe the propagation of solitons in various physical contexts, the most historically famous being for shallow water waves in a rectangular canal. Using subscripts to denote partial derivatives with respect to the distance x traveled and the time t elapsed, the KdV equation for the (normalized) transverse displacement ψ of the water waves is

$${\psi _t} + \alpha \psi {\psi _x} + {\psi _{xxx}} = 0$$

(10.1)

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Humor is emotional chaos remembered in tranquility.

James Thurber (1894-1961), American humorist.