| Abstract: |
| Many physical systems contain waves that are exponentially small in some asymptotic limit within the system. These waves are invisible to classical asymptotic power series methods, and require the application of sophisticated mathematical techniques known as exponential asymptotics. I will explain what exponential asymptotic techniques are, and how they can be used to extract and isolate these apparently inaccessible features of the physical systems. I will then outline how these techniques can be applied in order to:
\begin{enumerate}
\item Find nonlocal solitary waves (or nanoptera) in diatomic particle chains with nearest-neighbour interactions, using the Toda lattice as a particular example, and
\item Compute wave patterns caused by ships and submarines in the small Froude number limit (ie. when gravity dominates inertia).
\end{enumerate} |
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