Higher-order Boussinesq systems for two-way propagations of water waves

A class of higher-order approximations for the two-way propagation of surface water waves in a channel is derived. These systems, which generalize the classical Boussinesq equations, are formally equivalent and correct through second-order for small-amplitude, long wavelength surface motions. Preliminary analysis reveals significant mathematical differences between these model equations.

Min Chen (chen@math.purdue.edu)