A nonlinear Schrödinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrödinger equation (DNLS) on a periodic cubic lattice, which is a system of finitely many ordinary differential equations. We show that in two spatial dimensions, solutions to the DNLS converge strongly in L2 to those of the NLS as the grid size h> 0 approaches zero. As a result, the effectiveness of the finite difference method (FDM) is justified for the two-dimensional periodic NLS.
- Continuum limit
- Periodic nonlinear Schrödinger equation
- Uniform Strichartz estimate