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arXiv · 0903.4272

Higher order corrections for shallow-water solitary waves: elementary derivation and experiments

Gábor B. Halász
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Abstract

We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first-order equation is shown to be equivalent to the Korteweg-de Vries (KdV) equation, while the second-order equation is solved numerically. The propagation velocity found for the solitary waves of the second-order equation coincides with a known expression, but it is obtained in a simpler way. By measuring the propagation velocity of solitary waves in the laboratory, we demonstrate that the second-order theory gives a considerably improved fit to experimental results.

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Gábor B. Halász. 2009-09-13. Higher order corrections for shallow-water solitary waves: elementary derivation and experiments. https://doi.org/10.1088/0143-0807%2F30%2F6%2F009

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