High-Order Perturbation of Surfaces Short Course: Stability of Travelling Water Waves
In this contribution we present High-Order Perturbation of Surfaces (HOPS) methods as applied to the spectral stability problem for traveling water waves. The Transformed Field Expansion method (TFE) is used for both the traveling wave and its spectral data. The Lyapunov-Schmidt reductions for simple and repeated eigenvalues are compared. The asymptotics of modulational instabilities are discussed.
London Mathematical Society Lecture Note Series, 426
Akers, B. (2016). High-Order Perturbation of Surfaces Short Course: Stability of Traveling Water Waves. In T. Bridges, M. Groves, & D. Nicholls (Eds.), Lectures on the Theory of Water Waves (London Mathematical Society Lecture Note Series, pp. 51-62). Cambridge: Cambridge University Press. doi: https://doi.org/10.1017/CBO9781316411155.005