Normal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators
Abstract
Near an arbitrary finite gap potential we construct real analytic, canonical coordinates for the Benjamin-Ono equation on the torus having the following two main properties: (1) up to a remainder term, which is smoothing to any given order, the coordinate transformation is a pseudo-differential operator of order 0 with principal part given by a modified Fourier transform (modification by a phase factor) and (2) the pullback of the Hamiltonian of the Benjamin-Ono is in normal form up to order three and the corresponding Hamiltonian vector field admits an expansion in terms of para-differential operators. Such coordinates are a key ingredient for studying the stability of finite gap solutions of the Benjamin-Ono equation under small, quasi-linear perturbations.
Keywords
Cite
@article{arxiv.2109.02489,
title = {Normal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators},
author = {Thomas Kappeler and Riccardo Montalto},
journal= {arXiv preprint arXiv:2109.02489},
year = {2021}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1812.05391