We consider the nonlinear Schrödinger equation in dimension one with a nonlinearity concentrated in one point. We prove that this equation provides an infinite dimensional dynamical system. We also study the asymptotic behavior of the dynamics. We prove the existence of a global attractor for the system.

中文翻译：

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非线性集中在一点的非线性薛定谔方程的全局吸引子

我们考虑一维非线性薛定谔方程，非线性集中在一个点上。我们证明这个方程提供了一个无限维动力系统。我们还研究了动力学的渐近行为。我们证明了系统的全局吸引子的存在。