Solitary-wave solutions have been studied extensively over the years for the problems of gravity water waves, gravity-capillary waves, in two and three dimensions. They have been observed in nature and experiments, and have been analysed asymptotically and numerically. More recently, solitary waves have been also observed experimentally and investigated on liquid ferrofluid cylinders, see for example .
In this project, nonlinear waves in novel geometries will be studied. We will consider Plateau borders, which are microchannels obtained by merging three films inside liquid foams. Capillary jumps, solitary and periodic waves along Plateau borders in soap films have been observed experimentally [2,3], but there are far fewer theoretical studies available. The PhD project will aim first to perform a stability analysis of linear capillary waves propagating along the Plateau borders. Weakly nonlinear models such as Korteweg-de Vries  and nonlinear Schrodinger equations will then be derived formally near the critical speeds of the dispersion relation. Finally, a numerical scheme to compute solitary and periodic waves of the fully-nonlinear problem in this novel geometry will be built and comparisons with experimental and weakly nonlinear results will be performed.