Applications of KdV
The Korteweg-de Vries equation has touched on so varied a range of topics in ``abstract'' mathematics that it may be easy to overlook its origins and continuing applications in the applied sciences. The present paper is a fascinating and concise review of many such. In spite of the plethora of other integrable equations brought to birth over the past thirty years, the KdV remains a paradigm not only for our understanding of integrability but for many facets of the asymptotic analysis of physical phenomena. The author reviews the subjects of surface gravity waves, internal oceanic solitons, the acoustics of bubbly liquids, voidage in fluidized beds, magma flow and conduit waves, the great red spot on Jupiter, plasma physics and electrical transmission lines. In each case he discusses both theory and the experimental data, giving a critical appraisal of the successes of KdV theory. The diagnosis is a healthy one. Even in a case like the great red spot, where substantial problems remain, it seems clear that the KdV will play a key role in the final picture.
scientific article; zbMATH DE number 790790
scientific article