1 citations · 2 across the 6 of their papers we have counts for
8 papers
An explicit formula for the solution of the Benjamin-Ono equation and its applications
Louise Gassot, Patrick Gérard, Peter D. Miller
We summarize recent developments in the theory of the Benjamin-Ono equation, a well-known long-wave asymptotic model for internal waves in deep water, focusing on results obtained…
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…
Universality in the Small-Dispersion Limit of the Benjamin-Ono Equation
Elliot Blackstone, Peter D. Miller, Matthew D. Mitchell
We examine the solution of the Benjamin-Ono Cauchy problem for rational initial data in three types of double-scaling limits in which the dispersion tends to zero while simultaneou…
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…
On the Maxwell-Bloch System in the Sharp-Line Limit Without Solitons
Sitai Li, Peter D. Miller
We study the (characteristic) Cauchy problem for the Maxwell-Bloch equations of light-matter interaction via asymptotics, under assumptions that prevent the generation of solitons.…