The generalized regularized long wave (GRLW) equation is solved numerically by using a distributed approximating functional
(DAF) method realized by the regularized Hermite local spectral kernel. Test problems including propagation of single solitons,
interaction of two and three solitons, and conservation properties of mass, energy, and momentum of the GRLW equation are
discussed to test the efficiency and accuracy of the method. Furthermore, using the Maxwellian initial condition, we show that
the number of solitons which are generated can be approximately determined. Comparisons are made between the results of
the proposed method, analytical solutions, and numerical methods. It is found that the method under consideration is a viable
alternative to existing numerical methods.
This paper was supported by BradWelch, RidgeCape Capital,
Tokai, Cape Town.