This page will provide outlines of the lectures and links to printed notes. Click here to return to the main solitons web-page containing other course resources.
[ 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 Introduction |
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