# Derivation of the tight-binding approximation for time-dependent nonlinear Schr\"odinger equations

## TL;DR

This paper rigorously derives a tight-binding approximation for the nonlinear time-dependent Schrödinger equation with periodic potential, providing precise estimates of the approximation error in the large potential limit.

## Contribution

It establishes a mathematically rigorous connection between the continuous nonlinear Schrödinger equation and the discrete tight-binding model in a time-dependent setting.

## Key findings

- Validates the tight-binding approximation with explicit error bounds
- Shows the approximation holds in the large potential limit
- Bridges continuous and discrete models for nonlinear quantum dynamics

## Abstract

In this paper we consider the nonlinear one-dimensional time-dependent Schroedinger equation with a periodic potential and a local perturbation. In the limit of large periodic potential the time behavior of the wavefunction can be approximated, with a precise estimate of the remainder term, by means of the solution to the discrete nonlinear Schroedinger equation of the tight-binding model.