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arXiv · 1805.09049

Amplitude Decay of Solitary Waves - asymptotic and numerical results

Paul Hammerton·Dane Grundy
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Abstract

The relevance of perturbed forms of the Korteweg-de Vries equation to a range of physical problems is discussed. Solutions which are perturbations of solitary travelling wave solutions are then considered, focussing predominantly on the Burgers-Korteweg-de Vries equation. Asymptotic analysis demonstrates the appearance of a slowly decaying tail behind a core soliton-like solution. The solution in the tail region is determined in the form of a convolution integral involving the Airy function, while the core solution is obtained explicitly. Asymptotic results are fully validated by comparison with numerical results, obtained using a pseudospectral scheme.

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Paul Hammerton, Dane Grundy. 2018-05-23. Amplitude Decay of Solitary Waves - asymptotic and numerical results. https://arxiv.org/abs/1805.09049

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