Solitons

This is the web-page for the 2009-10 Solitons course. If you're looking for the remains of the 2008-9 page (which contains some photos from last year) please click here.

Animations and computer programs

• Click here to see numerical solutions of the "dispersing KdV" equation.
• Click here to see numerical solutions of the dispersionless KdV, or Monge, equation.
• Click here to see the animations of solutions of the full KdV equation from the second half of the first lecture.
  
• A python program written by Sam Webster for solving the KdV equation numerically, and his explanation of the numerical method he used.
• An animation of a wavepacket.
• Python programs to solve the sine-Gordon and phi^4 theories, which you'll need for problem 9.

Problem sheets

• Sheet 1 (please do problems 1,4,6 for Monday lunchtime)
• Sheet 2 (please do problems 8(d) and 9 for Friday suppertime)
• Sheet 3
• Sheet 4 (please do problems 11, 16(a),(b),(c) and 18 for Saturday suppertime)

Interesting links

• John Scott Russell
  A page about the discovery of the soliton
• Real solitons in the Strait of Gibraltar and on the Dordogne river
  
• Solitons in space
  A slightly less realistic -and less accurate- example of a soliton (from the Star Trek TV programme)
• Making waves - singly
  An article about the applications of solitons
• Mathematics at the turn of the millennium
  A general article about modern mathematics with some interesting comments about soliton theory about half-way down
• The Fermi-Pasta-Ulam problem was one of the reasons for the revival of interest in solitons in the 1960s. You can read some more about it here and here.
• The Solitons Homepage
  A very comprehensive set of links, with some animations
• Solitons and Soliton Collisions
  Covers sine-Gordon collisions, with very nice animations of the pendulum model discussed in lectures
• The Soliton-Lab Art Gallery
  Some more animations of KdV and SG solitons
• RVJ's Soliton Page
  A large set of links (though not all of them work)
• See this page for a description of the scattering of phi^4 kinks. This work was also described in a short 'journal club' article in Nature (scroll down the page to see the article).

Pictures

• Muizenberg walk
• Table Mountain
• Elephant Eye