Infinite-order multisoliton solutions to the Benjamin--Ono equation and soliton resolution

TL;DR

This paper constructs infinite-order multisoliton solutions for the Benjamin-Ono equation with slow decay initial data, demonstrating their long-time behavior as a superposition of independent solitons without radiation.

Contribution

It introduces a new class of infinite-order multisoliton solutions for the Benjamin-Ono equation and analyzes their asymptotic decoupling behavior.

Findings

Solutions decompose into independent solitons over time

No radiation term appears in the long-time limit

Handles initial data with slow spatial decay

Abstract

We construct a class of infinite-order multisoliton solutions of the Benjamin-Ono equation on the line, for which the initial data exhibits slow spatial decay. We prove that in the long-time asymptotics, such a solution decouples as an infinite superposition of independent soliton solutions with different velocities and no radiation term.