The goal of the integrable systems working seminar during the spring quarter will be on effective application of algebraic geometry and finite gap theory of integrable systems to problems in coastal and ocean engineering. We will use the textbook Algebro-Geometric Approach to Nonlinear Integrable Equations by Belokolos, Bobenko, Enol’skii, Its and Matveev as the main reference. We will also discuss “Comparative analysis of bore propagation over long distances using conventional linear and KdV-bases nonlinear Fourier transform” by Bruhl et al from 2022 to see how the methods from algebraic geometry can be applied to practical problems. The goal of this quarter will be to understand the solution to the KdV equation with a periodic trapezoidal bore initial condition using the theory of finite gap solutions. During the first meeting, I will introduce the sources, and then we can discuss a plan for further reading and presentations by participants.
Please email me if you would like to be informed of future meetings.