Asymptotic stability of solitons for the Benjamin-Ono equation

2008/03/26 by Kenig, C. E., Martel, Y. · 3 citations
#35B40 #35Q51 #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0803.3683

Abstract

In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of Martel and Merle (arXiv:0706.1174v2). As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.

Cited by

• Asymptotic stability of solitary waves for the b-family of equations
• A monotonicity formula for the fractional Laplacian and instability results for the Shrira equation
• Orbital stability of Benjamin--Ono multisolitons

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