Slowly Varying Solitary Wave Solutions of the Perturbed Korteweg‐de Vries Equation Revisited

Using a multi‐scale perturbation expansion we reconsider the slowly varying solitary wave asymptotic solution of the perturbed Korteweg‐de Vries equation. The well‐known results for the variation of the solitary‐wave amplitude and the accompanying trailing tail are recovered. Here the analysis is carried through to second order so as to determine a general expression for the first‐order speed correction. The result obtained here generalizes and improves previous results.