A DCAMM seminar will be presented by
Professor Erik Wahlén
Centre for Mathematical Sciences,
Lund University, Sweden
Abstract:
Although one of the most obvious examples of wave motion, water waves are remarkably challenging to study mathematically. This is due to the high degree of nonlinearity of the equations and the fact that the problem involves a free and moving boundary (the water surface). Travelling waves are special solutions which move at constant speed without change of shape and come in different forms, such as periodic or solitary waves. Such waves were described and computed formally by Airy, Stokes, Boussinesq, Lord Rayleigh, Korteweg & de Vries etc. in the 19th century, and then rigorously constructed as solutions to the water wave problem in the 20th century, including waves of large amplitude. In order to see these waves in real life, their stability properties are however also of fundamental importance. While formal work on the stability of solitary waves was published by Boussinesq already in 1872 and by Benjamin & Feir on periodic waves in 1967, rigorous theory for the full water wave problem has only developed in the last 30 years.
In my talk I will review recent results and methods and mention some open questions.
Cake, coffee and tea will be served 15 minutes before the seminar starts.
All interested persons are invited