Depth-integrated long-wave models, such as the shallow-water and Boussi-nesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it… (More)
The object of this article is the comparison of numerical solutions of the so-called Whitham equation describing wave motion at the surface of a perfect fluid to numerical approximations of solutions of the full Euler free-surface water-wave problem. The Whitham equation η t + 3 2 c 0 h 0 ηη x + K h0 * η x = 0 was proposed by Whitham  as an alternative… (More)
Watershed segmentation is useful for a number of image segmentation problems with a wide range of practical applications. Traditionally, the tracking of the immersion front is done by applying a fast sorting algorithm. In this work, we explore a continuous approach based on a geometric description of the immersion front which gives rise to a partial… (More)
Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion which govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the… (More)
The generalized regularized long-wave equation admits a family of negative solitary waves. The stability of these waves is investigated by numerical simulation using a spectral discretization.
Solutions of a boundary value problem for the Korteweg–de Vries equation are approximated numerically using a finite-difference method, and a collocation method based on Chebyshev polynomials. The performance of the two methods is compared using exact solutions that are exponentially small at the boundaries. The Chebyshev method is found to be more… (More)
A matched asymptotic expansion is used to give a formal derivation of a number of systems of model equations for the evolution of interfacial waves subject to capillarity. For one of these systems, approximate solitary waves are found numerically, and the solutions are compared to the Benjamin equation which arises in the special case of one-way propagation.