Bulletin des Sciences Mathématiques· 2026Q1
A new class of critical solutions for 1D cubic NLS
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- Q1SCImago
- 2026year
Short summary
Researchers prove the existence of a new class of critical solutions for 1D cubic NLS with initial data as a sum of Dirac masses, specifically for critical regularity $F(L^\infty)$ and $\dot H^s$ with $s < -1/2$.
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Key points
- Proves existence of new critical solutions for 1D cubic NLS.
- Initial data is a sum of Dirac masses with critical regularity $F(L^\infty)$ and $\dot H^s$ ($s < -1/2$).
- Addresses a known gap for critical regularity initial conditions.
- Methodology involves a scattering approach, pseudo-conformal transformation, and oscillatory integral estimations.
AI-generated from the title and abstract; the full text is not read.
Abstract
The aim of this article is to prove the existence of a new class of solutions of 1D cubic NLS with an initial data related to a sum of Dirac masses, of critical regularity $F(L^\infty)$, and belonging to $\dot H^s$ for any $s <-1/2$. This problem is motivated by the lack of result for critical regularity initial condition. Our result is based on a scattering approach, after performing a pseudo-conformal transformation, and on fine estimations of oscillatory integrals.
The authors' abstract, as published at the source. Bulletin des Sciences Mathématiques, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics