Solitons and Solitary Waves
Formula of some solitary waves and solitons for the phi4,
sine-Gordon, and KdV nonlinear wave equations.
Some notes on finding solitary wave solutions;
Movies of some solutions;
The sine-Gordon solitons; kinks and breathers. In this page we see animations of the
breather and kink-antikink collision. We also see a simulation of a bound state of two kinks and notice how
similar it is to the breather. Can a breather solution to the phi4 equation be made from the
collision of two (phi4) kinks? To read more about this, begin with the references mentioned on this
web page.
Some references:
- Solitons, Claudio Rebbi. Scientific American, February 1979,
pages 92 - 116.
- Solitons: An Introduction, P.G. Drazin and R.S. Johnson.
Cambridge University Texts.
- Waves Called Solitons, Michel Remoissenet. Springer.
- Solitons and Nonlinear Wave Equations, R. Dodd, J. Eilbeck, J. Gibbon, H. Morris.
Academic Press, 1972.
Last updated: Nov 22
sine-Gordon kinks. This shows the collision of two kinks. Compare this with the movie below of
the collision of two kinks of the phi4 equation.
The stationary sine-Gordon breather. This a time-periodic soliton.
The travelling sine-Gordon breather.
The KdV travelling soliton.
The KdV travelling breather. This is a time-periodic soliton.
Solution of the sine-Gordon equation with arbitrary initial data. Here we see the
resolution of the solution into kinks and breathers (see Strauss page 369 - 372).
The collision of two KdV solitons. Notice how the structures of the solitons remain
unchanged by the collision.