论文标题
具有潜力的矩阵非线性schrödinger方程
The Matrix Nonlinear Schrödinger Equation with a Potential
论文作者
论文摘要
本文专门研究针对基质非线性schrödinger方程的小解决方案的大型渐近学，在半线和一般的自助会边界条件上具有潜力，并且在整个超临界状态下具有潜力和一般点相互作用的线路。我们证明，小型解决方案是散射解决方案，这些解决方案在及时渐近，$ t \ to \ pm \ infty，$ cy是对相关的线性矩阵Schrödinger方程的解决方案，而潜在的方程相同。潜力可以是通用的或例外的。我们的方法基于具有潜力的相关线性矩阵schrödinger方程的光谱和散射理论的详细结果，并以一种使我们能够以适当规范为基础的分解技术。
This paper is devoted to the study of the large-time asymptotics of the small solutions to the matrix nonlinear Schrödinger equation with a potential on the half-line and with general selfadjoint boundary condition, and on the line with a potential and a general point interaction, in the whole supercritical regime. We prove that the small solutions are scattering solutions that asymptotically in time, $t \to\pm\infty, $ behave as solutions to the associated linear matrix Schrödinger equation with the potential identically zero. The potential can be either generic or exceptional. Our approach is based on detailed results on the spectral and scattering theory for the associated linear matrix Schrödinger equation with a potential, and in a factorization technique that allows us to control the large-time behaviour of the solutions in appropriate norms.
