Solitary water waves
25 november 2016 13:15 T129, Teknikhuset
Speaker
Docent Erik Wahlén, Centre for Mathematical Sciences, Faculty of Science, Lund University.
Abstract
The theory of solitary waves (or solitons) has its origin in the observation of a solitary water wave by John Scott Russell in 1834 and his subsequent experiments. His findings were explained mathematically in the framework of the Korteweg-de Vries (KdV) equation at the end of the 19th century. The KdV equation can be derived as an asymptotic model for small-amplitude shallow water waves starting from the equations of ideal fluid dynamics with a free surface. In this talk I will discuss what can be said about solitary waves for the original hydrodynamical problem, without making the small-amplitude shallow-water approximation. If surface tension is included, there is a wide variety of solitary waves, including two-dimensional wave patterns which decay in every horizontal direction. I will give some ideas of the mathematical methods involved without getting too technical.