Analytical and numerical solutions to initial-boundary value problems of the water wave motion in a reservoir.
Approximate traveling wave solutions of coupled Whitham-Broer-Kaup shallow water equations by homotopy analysis method.
Asymptotic analysis of surface waves due to high-frequency disturbances
The present paper is devoted to the asymptotic analysis of the linear unsteady surface waves. We study two problems concerned with high-frequency surface and submerged disturbances. The two-scale asymptotic series are obtained for the velocity potential. The principal terms in the asymptotics of some hydrodynamical characteristics of the wave motion (the free surface elevation, the energy, etc.) are described.
Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions.
Asymptotic behaviour of solutions to the Korteweg-deVries-Burgers system
Benjamin–Ono periodic bifurcating water waves in presence of an essential spectrum
Bifurcation and symmetry in problems of capillary-gravity waves.
Comparaison entre modèles d'ondes de surface en dimension 2
Partant du principe de conservation de la masse et du principe fondamental de la dynamique, on retrouve l'équation d'Euler nous permettant de décrire les modèles asymptotiques de propagation d'ondes dans des eaux peu profondes en dimension 1. Pour décrire la propagation des ondes en dimension 2, Kadomtsev et Petviashvili [ 15 (1970) 539] utilisent une perturbation linéaire de l'équation de KdV. Mais cela ne précise pas si les équations ainsi obtenues dérivent de l'équation d'Euler, c'est ce que...
Computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators.
Conservation laws for shallow water waves on a sloping beach.
Construction de solutions pour les équations de Korteweg-de Vries généralisées
Control of the surface of a fluid by a wavemaker
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
Control of the surface of a fluid by a wavemaker
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in Lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
Damping of waves due to a soluble film.
Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves
This note is devoted to the study of a bi-fluid generalization of the nonlinear shallow-water equations. It describes the evolution of the interface between two fluids of different densities. In the case of a two-dimensional interface, this systems contains unexpected nonlocal terms (that are of course not present in the usual one-fluid shallow water equations). We show here how to derive this systems from the two-fluid Euler equations and then show that it is locally well-posed.
Dual integral equations -- revisited.
Effects of diffraction and radiation on a submerged sphere.
Exact boundary controllability of a nonlinear KdV equation with critical lengths
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
Existence by minimisation of solitary water waves on an ocean of infinite depth
Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation.