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Article Dans Une Revue Annales de l'Institut Henri Poincaré C, Analyse non linéaire Année : 2021

Existence of multi-solitons for the focusing Logarithmic Non-Linear Schrodinger Equation

Résumé

We consider the logarithmic Schrödinger equation (logNLS) in the focusing regime. For this equation, Gaussian initial data remains Gaussian. In particular, the Gausson-a time-independent Gaussian function-is an orbitally stable solution. In this paper, we construct multi-solitons (or multi-Gaussons) for logNLS, with estimates in $H^1 \cap \mathcal{F} (H^1)$. We also construct solutions to logNLS behaving (in $L^2$) like a sum of $N$ Gaussian solutions with different speeds (which we call multi-gaussian). In both cases, the convergence (as $t \rightarrow \infty$) is faster than exponential. We also prove a rigidity result on these multi-gaussians and multi-solitons, showing that they are the only ones with such a convergence.
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Dates et versions

hal-02498540 , version 1 (04-03-2020)

Identifiants

Citer

Guillaume Ferriere. Existence of multi-solitons for the focusing Logarithmic Non-Linear Schrodinger Equation. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2021, 38 (3), pp.841-875. ⟨10.1016/j.anihpc.2020.09.002⟩. ⟨hal-02498540⟩
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