Weakly nonlinear theory for dispersive waves generated by moving seabed deformation

Computational Models for Weakly Dispersive Nonlinear Water Waves

Numerical methods for the two and three dimensional Boussinesq equations governing weakly non-linear and dispersive water waves are presented and investigated. Convenient handling of grids adapted to the geometry or bottom topography is enabled by nite element discretization in space. Staggered nite diierence schemes are used for the temporal dis-cretization, resulting in only two linear system...

Water waves generated by a moving bottom

Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.

Nonlinear Dispersive Waves on Trees

We investigate the well-posedness of a class of nonlinear dispersive waves on trees, in connection with the mathematical modeling of the human cardiovascular system. Specifically, we study the Benjamin-Bona-Mahony (BBM) equation, also known as the regularized long wave equation, posed on finite trees, together with standard junction and terminal boundary conditions. We prove that the Cauchy pro...

Semiclassical Asymptotics for Weakly Nonlinear Bloch Waves

We study the simultaneous semi-classical and adiabatic asymptotics for a class of (weakly) nonlinear Schrödinger equations with a fast periodic potential and a slowly varying confinement potential. A rigorous two-scale WKB–analysis, locally in time, is performed. The main nonlinear phenomenon is a modification of the Berry phase.

Slow Passage through Resonance for a Weakly Nonlinear Dispersive Wave