Uniqueness of standing-waves for a non-linear Schr "odinger equation\n with three pure-power combinations in dimension one

2017/09/02 by Daniele Garrisi, Garrisi, Daniele, Vladimir Georgiev +1
Mathematics · Physics and Astronomy · #35Q55 #47J35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1709.00586

openalex publication_date 2017/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that symmetric and positive profiles of ground-state standing-wave of\nthe non-linear Schr "odinger equation are non-degenerate and unique up to a\ntranslation of the argument and multiplication by complex numbers in the unit\nsphere. The non-linear term is a combination of two or three pure-powers. The\nclass of non-linearities satisfying the mentioned properties can be extended\nbeyond two or three power combinations. Specifically, it is sufficient that an\nEuler differential inequality is satisfied and that a certain auxiliary\nfunction is such that the first local maximum is also an absolute maximum.\n

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