Continuum limit for discrete NLS with memory effect

10/13/2019

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by   Ricardo Grande, et al.

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We consider a discrete nonlinear Schrödinger equation with memory effect on the lattice hZ with mesh-size h>0. As h→ 0, we prove that solutions to this discrete equation converge strongly in L^2 to the solution to a continuous NLS-type equation with a memory effect, and compute the precise rate of convergence. In the process, we extend some recent ideas proposed by Hong and Yang in order to exploit a smoothing effect. This approach could therefore be adapted to tackle continuum limits of more general dispersive equations that require working in similar spaces.