A comparison of solutions of two model equations for long waves
Abstract
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 surfacewave phenomena in openchannel flows. The purpose of the present paper is to make a quantitative comparison between the solutions to the initialvalue 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.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 February 1983
 Bibcode:
 1983STIN...8334238B
 Keywords:

 Boundary Value Problems;
 Channel Flow;
 Surface Waves;
 Wave Equations;
 Wave Propagation;
 Comparison;
 Computation;
 Fourier Transformation;
 Mathematical Models;
 Partial Differential Equations;
 Solutions;
 Fluid Mechanics and Heat Transfer