P. D. Miller

activity

20242026

collaborators

5 papers

math.AP2026

The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality

Louise Gassot, Patrick GÃ©rard, Peter D. Miller

We obtain the leading term in the solution of the Cauchy problem for the Benjamin-Ono equation in the limit $t \to + \infty$ with $x = O (t^{1/2})$ . We show that the rate of decay exceed…

math.AP2026

A proof of the soliton resolution conjecture for the Benjamin--Ono equation

Louise Gassot, Patrick GÃ©rard, 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…

math.AP2025

The Benjamin-Ono Initial-Value Problem for Rational Data with Application to Long-Time Asymptotics and Scattering

Elliot Blackstone, Louise Gassot, Patrick GÃ©rard +1

We show that the initial-value problem for the Benjamin-Ono equation on $R$ with $L^{2} (R)$ rational initial data with only simple poles can be solved in closed for…

math.AP2024

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…

math.AP2024

The Benjamin-Ono equation in the zero-dispersion limit for rational initial data: generation of dispersive shock waves

The leading-order asymptotic behavior of the solution of the Cauchy initial-value problem for the Benjamin-Ono equation in $L^{2} (R)$ is obtained explicitly for generic rati…