Scattering of internal waves in a two-dimensional channel

I will describe joint work with Zhenhao Li and Jian Wang on the scattering of internal waves in a two-dimensional channel with flat ends. We obtain the uniqueness of appropriately defined outgoing solutions, and consequently show that a scattering matrix exists and may be regarded as a smoothing perturbation of a « bounce map » obtained from ray-tracing. We moreover obtain a limiting absorption principle which allows us to describe long-time asymptotics of of solutions.