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 $t\to \infty$) is faster than exponential. We also prove a rigidity result on these constructed multi-gaussians and multi-solitons, showing that they are the only ones with such a convergence.

我们考虑聚焦系统中的对数Schrödinger方程（logNLS）。对于该方程式，高斯初始数据仍为高斯。特别是，与时间无关的高斯函数高斯（Gausson）是轨道稳定的解决方案。在本文中，我们为logNLS构造了多孤子（或多高斯），其估计为$H^{\mathrm{1个}}\cap \mathcal{F}（H^{\mathrm{1个}}）$。我们还构建了logNLS行为的解决方案（在${\mathrm{大号}}^{\mathrm{2个}}$），例如N个具有不同速度的高斯解决方案的总和（我们称其为多高斯）。在这两种情况下，收敛（如$Ť\to \infty$）比指数快。我们还证明了这些构造的多高斯和多孤子的刚度结果，表明它们是唯一具有这种收敛性的结果。