Abstract
We derive the approximate form and speed of a solitary-wave
solution to a perturbed KdV equation. Using a conventional perturbation
expansion, one can derive a first-order correction to the solitary-wave speed,
but at the next order, algebraically secular terms appear, which produce
divergences that render the solution unphysical. These terms must be treated by
a regrouping procedure developed by us previously. In this way, higher-order
corrections 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
there is only one possible solitary wave that has a form similar to the
unperturbed soliton solution.
Publisher
Cambridge University Press (CUP)
Cited by
10 articles.
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