Patrik Nabelek, Oregon State University
I will discuss various applications of Hamiltonian and completely integrable systems to the theory of deterministic and stochastic waves, and related areas, such as wave structure interactions. I will begin with the problem of generating a time series in an experimental basin mimicking a given JONSWAP spectrum (Hasselmann et al 1973) with applications to testing floating structures and optimal control of wave energy converters in mind. I will discuss recent work by Mohtat, Yim, Osborne 2021 addressing this problem by using the inverse scattering transform for the nonlinear Schrödinger equation. The next part will contain some recent results on analytical solutions to the Korteweg-de Vries equation describing interactions of a large number of solitons. I will also discuss the extensions of this approach to the Kaup-Broer system and the Kadomtsev-Petviashvili equation. This part is based off various papers with various coauthors related to my dissertation work with Vladimir Zakharov, and Ken McLaughlin. I will end with a discussion of a collaborative work in progress with Yim on the use of infinite dimensional Hamiltonian dynamical systems theory for the analysis of wave-wave and wave-structure interactions to inform solutions to design problems in ocean and coastal engineering.
Joint work with Solomon Yim (Coastal and Ocean Engineering), Oregon State University.