Solitons

This is the web-page for the 2025-26 level III Solitons course in the Michaelmas term. See also the blackboard page for the course.

[ Contact · Lectures · Office hour · Problems classes · Animations · Problems · Assignments · Books · Links · Dramatis personae ]

Contact

• Patrick Dorey
• Room No: MCS 2033
• email: p.e.dorey@durham.ac.uk

Lectures

• Tuesday 9:00 and Friday 16:00, both in MCS2068
• Lecture outlines

Office hour

• Tuesday 10:00 in MCS2033
  (If you have a question and can't make it then, please send me an email and we can fix up an alternative.)

Problems classes

• Wednesday 11:00 in MCS2068 in teaching weeks 4, 6, 8 and 10
  • Week 4: problems 10, 17, 14

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 numerical solutions of the full KdV equation.
• Click here to see the other animations, of solutions of the full KdV equation, that will be discussed in the first lecture.
  (Warning - these may slow down your computer while they load!)
• An animation of a wavepacket.
• Another wavepacket, showing the effect of dispersion.
• A python program to solve the KdV equation numerically.

Problems

• Problem set 1 (problems 1-17)
• Problem set 2 (problems 18-30)
• Useful integrals

Assignments

Assignments will be set every week, but only the even-numbered ones will be for handing in. Solutions to all will be posted on blackboard as term goes by.

• Week 1: problems 1 and 2
• Week 2: problems 4 and 11, to be submitted on gradescope by 12 noon on Monday 20/10/25
• Week 3: problems 10 and 13
• Week 4: problem 15, to be submitted on gradescope by 12 noon on Monday 3/11/25

Recommended books

• P.G. Drazin and R.S. Johnson, Solitons: An Introduction, CUP 1989; ISBN 0521336554
• N. Manton and P. Sutcliffe, Topological Solitons, CUP 2004; ISBN 0521838363
• T. Dauxois and M. Peyrard, Physics of Solitons, CUP 2006; ISBN 0521854210

Interesting links

• John Scott Russell
  A page about Scott Russell and his discovery of the soliton
• Making waves
  Some more about the discovery of the soliton (h/t Stefano)
• Real solitons in the Strait of Gibraltar and on the Dordogne river
  
• Solitons in space
  A slightly less realistic -and much less accurately-described - example of a soliton (from this episode of the Star Trek TV programme)
• Solitons in South Africa
  A video made with students from the African Institute for Mathematical Sciences
• The Solitons Homepage
  
• 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-Tsingou problem
  This was one of the reasons for the revival of interest in solitons in the 1960s. You can read some more about it here
• Tsunamis
  An article about the equations which describe Tsunamis (including some comments on the links - or not - with solitons)
• A soliton haiku, written by Peter Lax, along with a nice animation of two KdV solitons colliding. (The haiku appears at the end of this interview with Lax)

Dramatis personae

Click on the mugshots to find out more...