Construction of quasi-periodic solutions for the quintic Schrödinger equation on the two-dimensional torus $\mathbb {T}^2$
Construction of quasi-periodic solutions for the quintic Schrödinger equation on the two-dimensional torus $\mathbb {T}^2$
In this paper, we develop an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional Hamiltonian systems. As an application of the theorem, we study the quintic nonlinear Schrödinger equation on the two-dimensional torus \begin{equation*} {\mathrm {i}}u_{t}-\Delta u + {|u|}^4u = 0,\quad x\in \mathbb {T}^2\coloneq \mathbb {R}^2/(2\pi \mathbb {Z})^2,\quad t\in \mathbb {R}. …