6 papers
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…
A proof of the soliton resolution conjecture for the Benjamin--Ono equation
Louise Gassot, Patrick Gérard, Peter D. Miller
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…
The Benjamin-Ono equation in the zero-dispersion limit for rational initial data: generation of dispersive shock waves
Elliot Blackstone, Louise Gassot, Patrick Gérard +1
The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in is obtained explicitly for generic rati…
The Benjamin-Ono Initial-Value Problem for Rational Data with Application to Long-Time Asymptotics and Scattering
Elliot Blackstone, Louise Gassot, Patrick Gérard +1
We show that the initial-value problem for the Benjamin-Ono equation on with rational initial data with only simple poles can be solved in closed for…
On Strong Zero-Dispersion Asymptotics for Benjamin-Ono Soliton Ensembles
Elliot Blackstone, Louise Gassot, Peter D. Miller
A soliton ensemble is a particular kind of approximation of the solution of an initial-value problem for an integrable equation by a reflectionless potential that is well adapted t…
Long time behavior of solutions for a damped Benjamin-Ono equation
Louise Gassot
We consider the Benjamin-Ono equation on the torus with an additional damping term on the smallest Fourier modes (cos and sin). We first prove global well-posedness of this equatio…