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Peer-reviewedCC BYSéminaire Laurent Schwartz — EDP et applications

Disproving the Deift conjecture: the loss of almost periodicity

  • Andreia Chapouto
  • Rowan Killip
  • Monica Vişan
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Abstract

In this note we present a result from [CKV24] related to a conjecture of Deift from 2008, who posited that almost periodic initial data leads to almost periodic solutions to the Korteweg-de Vries equation (KdV). We show that this is not always the case. Building on the new observation that the conjecture fails for the Airy equation, we construct almost periodic initial data whose KdV evolution remains bounded, but loses almost periodicity at a later time. This text is based on a Laurent Schwartz seminar given by the first author in November 2024, which in turn is based on joint work with Rowan Killip and Monica Vişan.

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Cite

BibTeXRIS
BibTeX
@article{chapouto2026disproving,
  title = {{Disproving the Deift conjecture: the loss of almost periodicity}},
  author = {Andreia Chapouto and Rowan Killip and Monica Vişan},
  journal = {Séminaire Laurent Schwartz — EDP et applications},
  year = {2026},
  month = nov,
  doi = {10.5802/slsedp.178},
  url = {https://hal.science/hal-05851881v1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Disproving the Deift conjecture: the loss of almost periodicity
AU  - Andreia Chapouto
AU  - Rowan Killip
AU  - Monica Vişan
PY  - 2026
DA  - 2026/11/04
JO  - Séminaire Laurent Schwartz — EDP et applications
DO  - 10.5802/slsedp.178
UR  - https://hal.science/hal-05851881v1
AB  - In this note we present a result from [CKV24] related to a conjecture of Deift from 2008, who posited that almost periodic initial data leads to almost periodic solutions to the Korteweg-de Vries equation (KdV). We show that this is not always the case. Building on the new observation that the conjecture fails for the Airy equation, we construct almost periodic initial data whose KdV evolution remains bounded, but loses almost periodicity at a later time. This text is based on a Laurent Schwartz seminar given by the first author in November 2024, which in turn is based on joint work with Rowan Killip and Monica Vişan.
SN  - 3076-8713
ER  -