5 papers
The half-wave maps equation on : Global well-posedness in and almost periodicity
Patrick Gérard, Enno Lenzmann
We consider the half-wave maps equation for , where $\mat…
The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality
Louise Gassot, Patrick Gérard, Peter D. Miller
We obtain the leading term in the solution of the Cauchy problem for the Benjamin-Ono equation in the limit with . We show that the rate of decay exceed…
An Explicit Formula for the Benjamin-Ono Hierarchy with Applications to Traveling Waves and Zero-Dispersion Limits
Patrick Gérard, Jiao He
In this paper, we first extend the explicit formula \cite{gerard2023explicit} for the classical Benjamin-Ono equation to each flow of the Benjamin-Ono hierarchy on line. We then us…
Infinite-order multisoliton solutions to the Benjamin--Ono equation and soliton resolution
Louise Gassot, Patrick Gérard, Patrick Gérard
We construct a class of infinite-order multisoliton solutions of the Benjamin-Ono equation on the line, for which the initial data exhibits slow spatial decay. We prove that in the…
A proof of the soliton resolution conjecture for the Benjamin--Ono equation
Louise Gassot, Patrick Gérard, Patrick Gérard +1
We give a proof of the soliton resolution conjecture for the Benjamin--Ono equation, namely every solution with sufficiently regular and decaying initial data can be written as a f…