A solitary-wave solution to a perturbed KdV equation

We derive the approximate form and speed of a solitary-wave solution to a p erturbed KdV equation. Using a conventional perturbation expansion, one can derive a first-order correction to the solitary-wave speed, but at the nex t order, algebraically secular terms appear, which produce divergences that render the solution unphysical. These terms must be treated by a regroupin g procedure developed by us previously. in this way, higher-order correctio ns to the speed are obtained, along with a form of solution that is bounded in space. For this particular perturbed KdV equation, it is found that the re is only possible solitary wave that has a form similar to the unperturbe d soliton solution.