论文标题
Ablowitz--Ladik系统的连续限制
Continuum limit for the Ablowitz--Ladik system
论文作者
论文摘要
我们表明，Ablowitz--Ladik系统的解决方案将仅$ l^2 $初始数据收敛到立方非线性schrödinger方程的解决方案。此外，我们考虑了该晶格模型的初始数据，该晶格模型激发了离散分散关系的两个临界点附近的傅立叶模式，并证明了与非线性Schrödinger方程的脱钩系统的收敛。
We show that solutions to the Ablowitz--Ladik system converge to solutions of the cubic nonlinear Schrödinger equation for merely $L^2$ initial data. Furthermore, we consider initial data for this lattice model that excites Fourier modes near both critical points of the discrete dispersion relation and demonstrate convergence to a decoupled system of nonlinear Schrödinger equations.
