Juan M. Restrepo

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Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation u t + u x + (u p) x ? u xxt = 0: For p > 5, the equation has both stable and unstable solitary-wave solutions, according to the theory of Souganidis and Strauss. Using a high-order accurate numerical scheme for the approximation of(More)
An application of Pontryagin's Maximum Principle, data assimilation is used to blend possibly incomplete or nonuniformly distributed spatio-temporal observational data into geo-physical models. Used extensively in engineering control theory applications, data assimilation has relatively recently been introduced into meteorological forecasting,(More)
Description: This workshop will assess the current state-of-the-art and identify needs and opportunities for future research at the intersection of large-scale inverse problems and uncertainty quantification. It will bring together and cross-fertilize the perspectives of researchers in the areas of inverse problems and data assimilation, statistics,(More)
Considered here is a model equation put forward by Benjamin that governs approximately the evolution of waves on the interface of a two-uid system in which surface tension eeects cannot be ignored. Our principal focus is the traveling-wave solutions called solitary waves, and three aspects will be investigated. A constructive proof of the existence of these(More)
Described here is a path integral, sampling-based approach for data assimilation, of sequential data and evolutionary models. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution,(More)
We present a theory for the interactions of waves and currents which results from depth-averaging the wave-driven circulation model proposed by McWilliams and Restrepo. This circulation model couples the gravity wave eld to oceanic scale ows. It speciically identiies the the drift velocity due to the gravity waves as the primary eeect of waves on the(More)