Soliton resolution conjecture and soliton gases for the Benjamin-Ono equation with infinite-order multisolitons in the sharp well-posedness space

@misc{pan2026soliton,
  title = {{Soliton resolution conjecture and soliton gases for the Benjamin-Ono equation with infinite-order multisolitons in the sharp well-posedness space}},
  author = {Hong-Yu Pan and Shou-Fu Tian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38198},
  eprint = {2610.38198},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38198},
}

TY  - UNPB
TI  - Soliton resolution conjecture and soliton gases for the Benjamin-Ono equation with infinite-order multisolitons in the sharp well-posedness space
AU  - Hong-Yu Pan
AU  - Shou-Fu Tian
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38198
UR  - https://arxiv.org/abs/2610.38198
AB  - We prove the soliton resolution conjecture for infinite-order multisoliton solutions in the sharp well-posedness space H^s(ℝ), s>−1/2, and construct soliton gases in H^s(ℝ) with arbitrary s∈ℝ, for the Benjamin--Ono equation. In particular, our work addresses two important open problems about inverse spectral for Lax operator, including the problem of spectral characterization of infinite-order multisolitons and that of determining the range of their asymptotic parameters. A central ingredient of our work is a spectral decomposition adapted to rough initial data. This extends the global soliton--radiation description to weakly weighted H^s data while allowing infinite negative eigenvalues. Another important ingredient is a continuous norming action that extends finite inverse spectral shifts to gas limits while retaining a full continuous norming weight. Our framework provides a basis for studying infinite-order soliton resolution and the construction and asymptotics of soliton gases for nonlocal equations.
ER  -