Soliton Theory and the Direct Method


From Fall 2009 to Spring 2010 I attended Kobe University in Japan. There I studied
with Professor Ohta Yasuhiro. During my stay I learned about Solitons and in particular the
so-called Hirota Direct Method.

Here is the wikipedia page on Solitons.

The following are notes on the Direct Method.

Hirota Bilinear Method
Pfaffians and Determinants
Structure of Soliton Equations

Here are some pictures. You might recognize the famous "Great wave of Kanagawa." Perhaps an "ancient" soliton? There is also
a picture of me with Professor Ohta. Thirdly, a picture of me at Itsukushima, probably one of the most well-known shrines of Japan. Enjoy!





Below is an animation made in Mathematica of 3 soliton waves. Note how even though the waves collide, they retain their original shape. This is
an important characteristic of solitonic waves. (Sorry for the bad quality. I will try to fix this later...)