|SPEAKER||Yuji Kodama 教授（俄亥俄州立大學）|
|TITLE||Mathematics for Web-Like Patterns of Solitary Waves in Shallow Water|
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 wave patterns based on a two-dimensional nonlinear dispersive
wave equation called the KP equation invented by Kadomtsev and Petviashvili in 1970.
Recently a large variety of the exact solutions of the KP equation, referred to as 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 of the KP solitons 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.