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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…