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Journal Articles Tunisian Journal of Mathematics Year : 2023

Nonflat conformal blow-up profiles for the 1-dimensional critical nonlinear Schrödinger equation

Abstract

Abstract For the critical one-dimensional nonlinear Schrödinger equation, we construct blow-up solutions that concentrate a soliton at the origin at the conformal blow-up rate, with a nonflat blow-up profile. More precisely, we obtain a blow-up profile that equals ∣ ∣ x ∣ ∣ + i κ x 2 near the origin, where κ is a universal real constant. Such profile differs from the flat profiles obtained in the same context by Bourgain and Wang in 1997.

Dates and versions

hal-04439882 , version 1 (05-02-2024)

Identifiers

Cite

Yvan Martel, Ivan Naumkin. Nonflat conformal blow-up profiles for the 1-dimensional critical nonlinear Schrödinger equation. Tunisian Journal of Mathematics, 2023, 5 (3), pp.505-572. ⟨10.2140/tunis.2023.5.505⟩. ⟨hal-04439882⟩
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