The authors prove a spectral dichotomy for Benjamin-Ono solutions in L2 and use it to obtain asymptotic stability of multisolitons.
Orbital stability of Benjamin--Ono multisolitons
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We show that multisoliton solutions to the Benjamin--Ono equation are uniformly orbitally stable in $H^s(\mathbb{R})$ for every $-\tfrac12<s\leq \frac12$. This improves the regularity required for stability up to the sharp well-posedness threshold; previous work (even on single solitons) had required $s\geq \frac12$. One key ingredient in our argument is a new variational characterization of multisolitons. A second ingredient is the extension to low-regularity slowly-decaying solutions of the Wu identity on eigenfunctions of the Lax operator. This extension also allows us to clarify the spectral type of the Lax operator for such potentials by precluding embedded eigenvalues.
fields
math.AP 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Explicit L^∞ asymptotic error formulas are established for the soliton resolution of the Benjamin-Ono equation in finite- and infinite-order multisoliton regimes.
citing papers explorer
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Asymptotic stability of Benjamin--Ono multisolitons in $L^2(\mathbb R)$
The authors prove a spectral dichotomy for Benjamin-Ono solutions in L2 and use it to obtain asymptotic stability of multisolitons.
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Soliton resolution conjecture for the Benjamin-Ono equation: Explicit $L^\infty$ asymptotic error formula
Explicit L^∞ asymptotic error formulas are established for the soliton resolution of the Benjamin-Ono equation in finite- and infinite-order multisoliton regimes.