论文标题
在多泡爆炸和多solitons对（随机）聚焦非线性schrödinger方程的最新进展
Recent progress on multi-bubble blow-ups and multi-solitons to (stochastic) focusing nonlinear Schrödinger equations
论文作者
论文摘要
我们回顾了与较低顺序扰动的一般类型$ l^2 $至关重要的非线性schrödinger方程（NLS）的长期行为的最新进展。两个规范模型是由线性乘法噪声和经典确定性NLS驱动的随机NLS。我们展示了相应的爆炸解决方案和孤子的构建和独特性，包括多泡泡沫 - 瓦型爆破溶液和非纯净的多solitons，这为质量量化猜想和孤子分辨率猜想提供了新的示例。还审查了纯种多泡爆炸和在非常低的渐近速率下的纯多泡爆炸和纯多solitons的精致唯一性。最后，作为一个新的结果，我们证明了随机爆破溶液的定性特性，包括质量的浓度，临界质量爆炸曲线的通用性以及在爆破时病毒的消失。
We review the recent progress on the long-time behavior for a general class of focusing $L^2$-critical nonlinear Schrödinger equations (NLS) with lower order perturbations. Two canonical models are the stochastic NLS driven by linear multiplicative noise and the classical deterministic NLS. We show the construction and uniqueness of the corresponding blow-up solutions and solitons, including the multi-bubble Bourgain-Wang type blow-up solutions and non-pure multi-solitons, which provide new examples for the mass quantization conjecture and the soliton resolution conjecture. The refined uniqueness of pure multi-bubble blow-ups and pure multi-solitons to NLS under very low asymptotical rate is also reviewed. Finally, as a new result, we prove the qualitative properties of stochastic blow-up solutions, including the concentration of mass, universality of critical mass blow-up profiles, as well as the vanishing of the virial at the blow-up time.
