SOLITONS INDUCED BY BOUNDARY-CONDITIONS FROM THE BOUSSINESQ EQUATION

Solitons induced by boundary excitation were first investigated numerically by Bona et al. [Philos. Trans. R. Soc. London, Ser. A 302, 457 (1981)] and by Chu et al. [Commun. Pure Appl. Math. 36, 495 (1983)] using the Korteweg-de Vries (KdV) equation. In this paper, their work is extended by considering various time-dependent boundary conditions and different unperturbed water depths. Then solitons induced from Boussinesq equations under similar conditions are studied, in order to remove the restriction in the KdV equation of propagation in only one direction. Thus soliton head-on collisions (as well as overtaking collisions) and reflections can be treated. The results from these two fully nonlinear equations are compared and they agree extremely well. The results of solitons induced by random boundary values are unexpected and particularly interesting. © 1990 American Institute of Physics.