| Abstract: |
| The 5th-order KdV equation is a PDE that describes shallow water waves with surface tension. The steady version of this problem is a canonical ODE problem in exponential asymptotics, studied by Akylas, Grimshaw & Joshi, and others, who demonstrated that the (symmetric) steady solution is unstable and cannot be reached by the time-varying PDE. Instead, the PDE features a burst of waves that propagate in one direction and cannot be described by the steady-state solution. With the advent of exponential asymptotics for PDEs, it is now possible to understand the evolution of the PDE system: the appearance of these rapidly propagating waves occurs due to Stokes' phenomenon in a small-time boundary layer. I will demonstrate the Stokes structure and show the form of these rapidly propagating waves. |
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