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[ Lecture outlines · Lecture notes · Extra material for Solitons V ]
Numbers in italics refer to sections (§)
or questions (Q) from the textbooks by
Drazin
and Johnson (DJ),
Manton and
Sutcliffe (MS), or
Dauxois and Peyrard (DP),
where you can
find out about the material to be covered.
| Week | Tuesday 9am MCS2068 | Friday 4pm MCS2068 |
| 1 |
1 Introduction 1.1 What is a soliton? The KdV equation DJ §1.1, §1.2; DP §1.1 |
Basic properties of solitons DJ §1.2, §1.3 1.2 The ball and box model |
| 2 |
2 Waves, dispersion and dissipation DJ §1.1 2.1 Dispersion Examples; phase and group velocities |
2.2 The Gaussian wavepacket 2.3 Dissipation DJ §1.1 2.4 Summary |
| 3 |
3 Travelling waves
DJ §2.1, §2.2
3.1 The KdV soliton 3.2 The sine-Gordon kink |
3.3 Physical model for the sine-Gordon kink DJ Q8.2; DP §2.1 |
| 4 |
4 Topological lumps and the Bogomolnyi bound 4.1 The sine-Gordon kink as a topological lump MS §5.3; DP §2.2.1 4.2 The Bogomolnyi argument MS §5.1 |
4.3 Summary 5 Conservation laws 5.1 The basic idea DJ §5.1.1 |
| 5 |
5.2 Example: conservation of energy for sine-Gordon 5.3 Conserved quantities for KdV DJ §5.1.1 |
5.4 The Gardner transform DJ §5.1.2 |
| 6 |
The Gardner transform (concluded) (NB: section 5.5, which you can find in the printed notes, is non-examinable bonus material) |
6 Bäcklund transformations DJ §5.4 6.1 Definition 6.2 A simple example |
| 7 |
6.3 The Bäcklund transformation for sine-Gordon DJ
§5.4.1 6.4 First example: the sG kink from the vacuum |
6.5 The theorem of permutability |