Stability in $H^{1/2}$ of the sum of $K$ solitons for the Benjamin-Ono equation

TL;DR

This paper proves the orbital stability in the energy space H^{1/2} of a sum of widely-spaced solitons for the Benjamin-Ono equation, ensuring their persistence without collisions.

Contribution

It establishes the orbital stability of multi-soliton solutions in H^{1/2} for the Benjamin-Ono equation, a novel result for this nonlocal dispersive PDE.

Findings

Stability of multi-soliton configurations in H^{1/2}

No collision occurs for widely-spaced solitons

Persistence of soliton structure over time

Abstract

This note proves the orbital stability in the energy space $H^{1/2}$ of the sum of widely-spaced 1-solitons for the Benjamin-Ono equation, with speeds arranged so as to avoid collisions.