Comparative effectiveness and patient-centered outcomes research: Enhancing uptake and use by patients, clinicians and payers

Second-order correct versions of the usual KdV-BBM models for unidirectional propagation of long-crested, surface water waves are considered here. The focus will be on a class of recently derived mathematical models for the propagation of such waves. A fully discrete, numerical algorithm based on the Fourier spectral method is developed and its convergence tested. We then use this algorithm to generate solitary- wave solutions to the model. While such waves are known to exist, exact formulas for them are not available. The heart of the paper is a sequence of numerical experiments aimed at understanding the stability of individual solitary waves, their interaction and whether or not the model exhibits resolution of general initial data into solitary waves. A comparison is made between the rst-order correct KdV-BBM models and the associated second order correct equations. A number of tentative conjectures pertaining to the models are put forward on the basis of these experiments.