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.