ANZIAM J.
44 (2002), 95102

Numerical solitary wave interaction: the order of the inelastic effect

T. R. Marchant
School of Mathematics and Applied Statistics
University of Wollongong
Wollongong NSW
Australia
tim@uow.edu.au



Abstract

Solitary wave interaction is examined using an
extended BenjaminBonaMahony (eBBM) equation.
This equation includes higherorder nonlinear and
dispersive effects and is is asymptotically
equivalent to the extended Kortewegde Vries
(eKdV) equation. The eBBM formulation is
preferable to the eKdV equation for the numerical
modelling of solitary wave collisions, due to
the stability of its finitedifference scheme. In
particular, it allows the interaction of steep
waves to be modelled, which due to numerical
instability, is not possible using the eKdV
equation.
Numerical simulations
of a number of solitary wave collisions of
varying nonlinearity are performed for two
special cases corresponding to surface water
waves. The mass and energy of the dispersive
wavetrain generated by the inelastic collision
is tabulated and used to show that the change in
solitary wave amplitude after interaction
is of , verifying previously obtained theoretical
predictions.

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