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.
Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation.
Existence of permanent and breaking waves for a shallow water equation : a geometric approach
The existence of global solutions and the phenomenon of blow-up of a solution in finite time for a recently derived shallow water equation are studied. We prove that the only way a classical solution could blow-up is as a breaking wave for which we determine the exact blow-up rate and, in some cases, the blow-up set. Using the correspondence between the shallow water equation and the geodesic flow on the manifold of diffeomorphisms of the line endowed with a weak Riemannian structure, we give sufficient...
Existence of solutions to the Rosenau and Benjamin-Bona-Mahony equation in domains with moving boundary.