P. D. Miller

collaborators

3 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

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…