论文标题
1D临界非线性schrödinger方程的非平原共形爆炸曲线
Non-flat conformal blow-up profiles for the 1D critical nonlinear Schrödinger equation
论文作者
论文摘要
对于临界的一维非线性schrödinger方程，我们构建了以共形的爆炸率以形式的爆炸解决方案，并具有非平原爆炸曲线。更确切地说，我们获得了一个等于$ | x |+iκX^2 $附近的爆炸配置文件，其中$κ$是一个通用的真实常数。这种轮廓不同于Bourgain和Wang [以关键非线性的非线性Schrödinger方程的构建爆炸解决方案的构建。安。 sc。规范。极好的。比萨CL。科学。 25（1997）]。
For the critical one-dimensional nonlinear Schrödinger equation, we construct blow-up solutions that concentrate a soliton at the origin at the conformal blow-up rate, with a non-flat blow-up profile. More precisely, we obtain a blow-up profile that equals $|x|+iκx^2$ near the origin, where $κ$ is a universal real constant. Such profile differs from the flat profiles obtained in the same context by Bourgain and Wang [Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity. Ann. Sc. Norm. Super. Pisa Cl. Sci. 25 (1997)].
