论文标题
存在用于聚焦对数非线性Schrodinger方程的多solitons
Existence of multi-solitons for the focusing Logarithmic Non-Linear Schrodinger Equation
论文作者
论文摘要
我们考虑对数schr {Ö} dinger方程（lognls）中的对数。对于此方程，高斯初始数据仍然是高斯。特别是，高森-A独立的高斯功能 - 是轨道稳定的解决方案。在本文中，我们为lognl构建了多solitons（或多功能仪），其中估计为$ h^1 \ cap \ mathcal {f}（h^1）$。我们还构建了以不同速度的$ n $ gaussian解决方案（我们称为多高斯）的$ n $ gaussian解决方案的总和。在这两种情况下，收敛（作为$ t \ rightarrow \ infty $）的速度都比指数快。我们还证明了这些多高斯和多solitons的刚性结果，这表明它们是唯一具有这种收敛性的人。
We consider the logarithmic Schr{ö}dinger 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.
