I am now in the throws of finishing my first post-PhD paper!! It will be co-authored with Denys Dutykh who helped me to fully understand the method used to derive the question in the first place. The next stage would be to have small amplitude waves in finite depth and then onto the weakly nonlinear stuff, which then would be another paper in itself. I also found a paper with the leaky dielectric model in who also worked on this stuff and derived their own weakly nonlinear equation and I lifted their evolution equation for the charge and managed to extend my results by a little.