Work

On the ground state of the nonlinear Schr{ö}dinger equation: asymptotic behavior at the endpoint powers

Year: 2025

Type: preprint

Abstract: We consider the ground states of the nonlinear Schr{ö}dinger equation, which stand for radially symmetric and exponentially decaying solutions on the full space. We investigate their behaviors at both endpoint powers of the nonlinearity, up to some rescaling to infer non-trivial limits. One case corresponds to the limit towards a Gaussian function called Gausson, which is the ground state of the stationary logarithmic Schr{ö}dinger equation. The other case, for dimension at least three, corresponds to the limit towards the Aubin-Talenti algebraic soliton. We prove strong convergence with explicit bounds for both cases, and provide detailed asymptotics. These theoretical results are illustrated with numerical approximations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2512.10690

Authors: Carles, Rémi, Chauleur, Quentin, Ferriere, Guillaume, Pelinovsky, Dmitry

Institutions: Institut de recherche mathématique de Rennes, Institut national de recherche en sciences et technologies du numérique, PARADYSE: Systèmes de particules et systèmes dynamiques, McMaster University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4417257592

Cites: 1

Cited by: 1

Related to: 10