Sneddon Lecture: Mathematics for web-like patterns of solitary waves in shallow water
Professor Yuji Kodama (Ohio State University)
Friday 23rd November, 2018 16:00-17:00 Western Infirmary Lecture Theatre (WILT)
We often observe web-like patterns of waves on the surface of shallow water. They are examples of nonlinear waves, and these patterns are generated by nonlinear interactions among several obliquely propagating solitary waves.
The aim of the talk is to explain these two-dimensional wave patterns based on a two-dimensional nonlinear dispersive wave equation called the KP equation invented by Kadomtsev and Petviashvili in 1970. These exact solutions are referred to as KP solitons. Recently a large variety of the KP solitons has been found and classified by using modern mathematical tools from several mathematical areas including algebraic geometry, algebraic combinatorics and representation theory.
In this talk, I will give a brief summary of the theory and, in particular, discuss an application to the Mach reflection problem in shallow water, which has an important implication to tsunami amplification along the shore. The problem describes the resonant interaction of solitary waves appearing in the reflection of an obliquely incident wave onto a vertical wall. The talk will be elementary and include many figures of the wave-patterns from real ocean data.