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arXiv · 1810.07183

Extended KdV equation for the case of uneven bottom

Piotr Rozmej·Anna Karczewska
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Abstract

We derived consistently, according to the second order perturbation approach, the extended KdV equation for an uneven bottom for the case of $\alpha=O(\beta)$ and $\delta=O(\beta^2)$. This equation can be obtained only when the bottom is given by a piecewise linear function. For the case of $\alpha=O(\beta)$ and $\delta=O(\beta)$, a unidirectional wave equation is derived in the first order approach with the same limitation for the bottom profile.

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Piotr Rozmej, Anna Karczewska. 2018-10-16. Extended KdV equation for the case of uneven bottom. https://arxiv.org/abs/1810.07183

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