  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.
