@article{Bambusi2024, 
author = {Dario Bambusi and Simone Paleari},
title = {A couple of BO equations as a normal form for the interface problem},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {23012-23026},
keywords = {water waves, Benjamin-Ono, Hamiltonian partial differential equations, normal form},
url = {https://www.sciopen.com/article/10.3934/math.20241118},
doi = {10.3934/math.20241118},
abstract = {We consider two fluids in a 2-dimensional region: The lower fluid occupies an infinitely depth region, while the upper fluid occupies a region with a fixed upper boundary. We study the dynamics of the interface between the two fluids (interface problem) in the limit in which the interface has a space periodic profile, is close to horizontal, and has a "long wave profile". We use a Hamiltonian normal form approach to show that up to corrections of second order, the equations are approximated by two decoupled Benjamin-Ono equations.}
}