Experimental studies of solitons in water
Jerry Bona has kindly supplied a list of some references in this area
with some comments. BBM stand for the Benjamin, Bona and Mahoney
equation, also known as the Regularized Long Wave equation, see
Phil. Trans. Roy. Soc. London, 272, 47-780, 1972, and
papers cited therein.
Zabusky, NJ and Galvin, C.J.: Shallow-water waves, the Korteweg-de Vries
equation and solitons, Journal of Fluid Mechanics, 47 , 1971,
811 - 824. Shows clearly the emergence of solitary waves. The Stokes
numbers here are pretty big on the other hand, so it is not a detailed
test of KdV or similar equations.
- Hammack, J.L.: A note on tsunamis: their generation and propagation in
an ocean of uniform depth, Journal of Fluid Mechanics, 60 1973,
769 - 799. He uses BBM as a model for tsunamis and does a nice set of
laboratory experiments where he generated the waves via a part of the
channel bottom that was moved up impulsively to simulate an underwater
- Hammack, J.L. & Segur, H.: The Korteweg-de Vries equation and water
waves. Part 2. Comparison with experiments, Journal of Fluid
Mechanics, 65 , 1974, 289 - 314. An analysis of
experimental data in the context of inverse scattering theory for KdV.
Svendsen, Ib.A. & Buhr Hansen, J.: On the deformation of periodic long
waves over a gently sloping bottom, Journal of Fluid Mechanics,
87 , 1978, 433 - 448. A look at how KdV-type equations work
over a variable bed - in particular, a shelving beach.
- Bona, J.L., Pritchard, W.G. and Scott, L.R., An evaluation of a model
equation for water waves, Phil. Trans. Roy. Soc. London,
302, 457-510, 1981.
A very careful look at BBM including dissipation and detailed
checks of accuracy.
Last Updated 29 Jan 2003 (JCE)
Chris Eilbeck/Heriot-Watt University, Edinburghemail@example.com