We numerically study nonlinear phenomena related to the dynamics of traveling
wave solutions of the Serre equations including the stability, the persistence,
the interactions and the breaking of solitary waves. The numerical method
utilizes a high-order finite-element method with smooth, periodic splines in
space and explicit Runge-Kutta methods in time. Other forms of solutions such
as cnoidal waves and dispersive shock waves are also considered. The
differences between solutions of the Serre equations and the Euler equations
are also studied.Comment: 28 pages, 20 figures, 3 tables, 33 references. Other author's papers
can be downloaded at http://www.denys-dutykh.com
