We construct radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schrödinger equation \(\text {i}\partial _t u + \Delta u + |u|^{p-1}u=0\) on \(\mathbb {R}^d\), close to the mass critical case and for any space dimension \(d\ge 1\). These profiles bifurcate from the ground-state solitary wave. The argument relies on the classical matched asymptotics method suggested in Sulem and Sulem (The nonlinear Schrödinger equation. Self-focusing and wave collapse. Applied mathematical sciences, 139, Springer, New York, 1999) which needs to be applied in a degenerate case due to the presence of exponentially small terms in the bifurcation equation related to the log–log blow-up law observed in the mass critical case.

我们构建径向对称的自相似吹胀型材质量超临界非线性薛定谔方程\（\文本{I} \局部_t U + \德尔塔U + | U | ^ {P-1} U = 0 \）上\ （\ mathbb {R} ^ d \），接近于质量临界情况并且对于任何空间尺寸\（d \ ge 1 \）。这些轮廓从基态孤立波分叉。该论点依赖于Sulem和Sulem中提出的经典匹配渐近方法（非线性Schrödinger方程。自聚焦和波崩。应用数学科学，139，Springer，纽约，1999），该方法需要在退化情况下应用与在质量临界情况下观察到的对数-对数爆炸法则有关的分叉方程中存在指数小项。