Pré-Publication, Document De Travail Année : 2026

On the ground state of the nonlinear Schrödinger equation: asymptotic behavior at the endpoint powers

Résumé

We consider the ground states of the nonlinear Schrödinger 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 Schrödinger 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.

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Dates et versions

hal-05409500 , version 1 (10-12-2025)
hal-05409500 , version 2 (11-03-2026)

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Rémi Carles, Quentin Chauleur, Guillaume Ferriere, Dmitry Pelinovsky. On the ground state of the nonlinear Schrödinger equation: asymptotic behavior at the endpoint powers. 2026. ⟨hal-05409500v2⟩
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