论文标题
soliton分辨率用于加权sobolev class中
Soliton resolution for equivariant self-dual Chern-Simons-Schrödinger equation in weighted Sobolev class
论文作者
论文摘要
我们考虑自我偶然的Chern-simons-schrödinger方程（CSS）在eprivariant对称性下，这是$ l^{2} $ - 关键方程。众所周知，（CSS）接纳了孤子和有限的爆破解决方案。在本文中，我们显示了在加权Sobolev空间中具有均衡数据的任何解决方案的Soliton分辨率$ h^{1,1} $：每个最大溶液最多分解为最多一个调制的孤子和辐射。一个惊人的事实是，非造成部分必须是单个调制的孤子。据我们所知，这是一类非线性schrödinger方程中孤子分辨率的第一个结果，这些结果是完全不可完全集成的。关键成分是孤子轮廓外部方程的散焦性质。这是（CSS）的两个独特特征的结果：自偶性和非本地非线性。
We consider the self-dual Chern-Simons-Schrödinger equation (CSS) under equivariant symmetry, which is a $L^{2}$-critical equation. It is known that (CSS) admits solitons and finite-time blow-up solutions. In this paper, we show soliton resolution for any solutions with equivariant data in the weighted Sobolev space $H^{1,1}$: every maximal solution decomposes into at most one modulated soliton and a radiation. A striking fact is that the nonscattering part must be a single modulated soliton. To our knowledge, this is the first result on soliton resolution in a class of nonlinear Schrödinger equations which are not known to be completely integrable. The key ingredient is the defocusing nature of the equation in the exterior of a soliton profile. This is a consequence of two distinctive features of (CSS): self-duality and non-local nonlinearity.
