A comparison of solutions of two model equations for long waves

This paper is concerned with mathematical models representing the unidirectional propagation of weakly nonlinear dispersive waves. Interest will be directed toward two particular models that are originally studied in the context of surface-wave phenomena in open-channel flows. The purpose of the present paper is to make a quantitative comparison between the solutions to the initial-value problem for each of these models. The basic conclusion of the study is that, on a long time scale T naturally related to the underlying physical situation, the equations predict the same outcome to within their implied order of accuracy. In this case the choice of one of these models over the other to describe a physical problem is apparently immaterial, with factors of incidental convenience probably providing the main criteria in a given situation.