Amplitude Decay of Solitary Waves - asymptotic and numerical results

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.