The objective of my talk is to describe the solitary wave of largest amplitude in the dispersive shock appearing in the solution of Riemann problem for dispersive equations describing non-linear long dispersive waves, in particular, the Benjamin-Bona-Mahony equation and Serre-Green-Naghdi equations. Such a large-amplitude solitary wave is the leading wave of the corresponding dispersive shock. Its speed and amplitude are defined analytically through the solitary limit of the corresponding Whitham modulation equations. In such a limit, Whitham's equations form a system of quasi-linear equations for which Riemann's invariants can be determined. The numerical results are in accordance with the analytical prediction.
By Matthew Juniper
By Sergey Gavrilyuk
By David Lannes
