On a nonlocal shallow water wave equation

par Gabriele Brüll (Norwegian University of Science and Technology)

mardi 21 mars 2017, 15:15 → 16:15 Europe/Paris

Fokko Du Cloux (Université Claude Bernard Lyon 1 - Campus de la Doua, Bâtiment Braconnier)

The Whitham equation is a nonlocal, nonlinear dispersive wave equation introduced by G. B. Whitham as an alternative wave model equation to the Korteweg-de Vries equation, describing the wave motion at the surface on shallow water. In this talk we introduce the Whitham equation and focus on its solitary wave solutions. In particular, we show that any solitary-wave solution is symmetric with exactly one crest from which the surface decreases exponentially. Moreover, the structure of the Whitham equation allows to conclude that conversely any unique symmetric solution constitutes a traveling wave. In fact, the latter result holds true for a large class of partial differential equations sharing a certain structure.