标题： 非保守非线性薛定谔方程可积子系统的准周期性与爆破 显示英文标题

标题： Quasiperiodicity and blowup in integrable subsystems of nonconservative nonlinear Schrödinger equations

摘要： 在本文中，我们研究一类非线性薛定谔方程$ i u_t = \triangle u + u^p $在$ x \in \mathbb{T}^d$上的动力学行为。 我们证明该偏微分方程在非负傅里叶系数的空间上是可积的，特别是解的每个傅里叶系数都可以通过求积法显式求解。 在这个子空间内，我们展示了大量（准）周期解，它们具有相同的频率，以及在$L^2$范数下有限时间内爆破的解。 显示英文摘要

摘要： In this paper, we study the dynamics of a class of nonlinear Schr\"odinger equation $ i u_t = \triangle u + u^p $ for $ x \in \mathbb{T}^d$. We prove that the PDE is integrable on the space of non-negative Fourier coefficients, in particular that each Fourier coefficient of a solution can be explicitly solved by quadrature. Within this subspace we demonstrate a large class of (quasi)periodic solutions all with the same frequency, as well as solutions which blowup in finite time in the $L^2$ norm.