The overarching goal of the proposed project is to understand the existence and stability of traveling wave solutions for asymptotic models appearing in water waves. Furthermore, the valitidy of the model equations shall be investigated. 

The main steps of the project are

1. Existence of fully-localized solutions for nonlocal water-wave model equations

2. Transverse stability of traveling waves in two-dimensional models

3. Existence of two-dimensional highest waves

4. Validity of asymptotic models in water waves