Shengqian Chen, University of North Carolina at Chapel Hill


Nonlinear water waves with periodic bottom topography

Abstract: Models of water waves with long wavelength under the assumption of no diffusion and no viscosity have been of great interest in literature for a long time. Both solitary and periodic traveling wave solutions have been studied in water layers of constant depth. However, in many realistic situations bottom topography plays an important role. Here, as a simple realization of a non-flat bottom we study how periodic topography can affect wave evolution, focussing in particular on solutions which are periodic in both space and time in the asymptotic regime of slowly varying depth. A numerical scheme based on an optimization method is implemented to obtain solutions that enforce space periodicity.

Mentor: Roberto Camassa (University of North Carolina at Chapel Hill)