On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d≥ 2

2009/02/04 by Dong Li, Xiaoyi Zhang, Li, Dong +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0902.0802

openalex publication_date 2009/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the focusing mass-critical NLS iu_t+Δu=-|u|^{\frac 4d}u, it is conjectured that the only global non-scattering solution with ground state mass must be a solitary wave up to symmetries of the equation. In this paper, we settle the conjecture for H¹_x initial data in dimensions d=2,3 with spherical symmetry and d≥ 4 with certain splitting-spherically symmetric initial data.

Citations

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Uniqueness of positive solutions of Δu−u+up=0 in Rn

Cited by

• Regularity of almost periodic modulo scaling solutions for mass-critical NLS and applications

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