# Nonlinear Stark-Wannier equation

## TL;DR

This paper investigates how nonlinear effects influence the energy spectrum of a one-dimensional Schrödinger equation with a periodic potential and external field, revealing complex bifurcation phenomena as nonlinearity increases.

## Contribution

It introduces a detailed analysis of bifurcations in nonlinear Stark-Wannier equations, highlighting the transition from discrete ladders to dense spectra in large potential regimes.

## Key findings

- Dense energy spectrum due to bifurcations
- Nonlinear effects cause cascade phenomena
- Transition from discrete to continuous spectra

## Abstract

In this paper we consider stationary solutions to the nonlinear one-dimensional Schroedinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark-Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs when the ratio between the effective nonlinearity strength and the tilt of the external field increases.