Internal structure of decaying solitary waves: Comparison of analytic and numerical results

The evolution of solitary waves governed by perturbations of the Korteweg-de Vries (KdV) equation is considered, focussing in particular on the Burgers-Korteweg-de Vries (BKdV) equation. Using matched asymptotic expansions the structure of the wave is determined for all timescales. A tail appears behind the main waveform, the structure of which is determined in the form of a convolution integral. Numerical results are presented using a pseudospectral scheme but modified so that linear terms are incorporated into an integrating factor. All details of the asymptotic structure of the waveform are validated by numerical results. Comparisons are made with earlier asymptotic analyses of decaying solitary waves.