We show that the nonlinear Schrödinger equation (NLSE) with white noise dispersion on quantum graphs is globally well-posed in $L^2$ once the free deterministic Schrödinger group satisfies a natural $L^1 - L^\infty$ decay, which is verified in many examples. Also, we investigate the well-posedness in the energy domain in general and in concrete situations, as well as the fact that the solution with white noise dispersion is the scaling limit of the solution to the NLSE with random dispersion.

中文翻译：

---

量子图上具有白噪声色散的非线性Schrödinger方程

我们显示，一旦自由确定性Schrödinger组满足自然的$ L ^ 1-L ^ \ infty $衰减，则在量子图上具有白噪声弥散的非线性Schrödinger方程（NLSE）在$ L ^ 2 $中处于全局良好位置。在许多示例中都得到了验证。此外，我们研究了一般情况和具体情况下能量域中的适定性，以及白噪声色散的解是随机色散的NLSE解的缩放极限。