Solitary wave interaction for the extended BBM equation

Abstract

Solitary wave interaction is examined, for the case of surface waves on shallow water, by using an extended Benjamin-Bona-Mahony (eBBM) equation. This equation includes higher-order nonlinear and dispersive effects, and hence is asymptotically equivalent to the extended Korteweg-de Vries (eKdV) equation. However, it has certain numerical advantages as it allows the modelling of steeper waves, which, due to numerical instability, is not possible using the eKdV equation. Numerical simulations of a number of collisions of varying nonlinearity are performed. The numerical results show evidence of inelastic behaviour at high order. For waves of small amplitude the evidence of inelastic behaviour ..