Beyond-all-orders effects in multiple-scales asymptotics: travelling-wave solutions to the Kuramoto-Sivashinsky equation

@article{Adams2003BeyondallordersEI,
  title={Beyond-all-orders effects in multiple-scales asymptotics: travelling-wave solutions to the Kuramoto-Sivashinsky equation},
  author={Kristl L. Adams and John R. King and Richard H. Tew},
  journal={Journal of Engineering Mathematics},
  year={2003},
  volume={45},
  pages={197-226}
}
This paper concerns the possible `shock' patterns that can exist in the solution to a singularly perturbed, third-order nonlinear ordinary differential equation arising as the travelling-wave reduction of the Kuramoto-Sivashinsky equation. In particular, the existence (or otherwise) of oscillatory shocks and multiple shocks made up of combinations of oscillatory and monotonic shocks is examined, using an optimal truncation strategy to track crucial exponentially small terms lying beyond all… CONTINUE READING
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