Stationary localized states due to nonlinear impurities described by the modified discrete nonlinear Schr\"odinger equation

TL;DR

This paper investigates stationary localized states in one-dimensional nonlinear lattices with impurities using the modified discrete nonlinear Schrödinger equation, analyzing their formation, stability, and phase diagrams across various impurity configurations.

Contribution

It introduces a comprehensive analysis of localized states in nonlinear lattices with different impurity types using the modified discrete nonlinear Schrödinger equation.

Findings

Localized states are not necessarily confined despite nonlinear impurities.

Phase diagrams reveal the conditions for state localization and stability.

States exhibit non-localization in systems with random nonlinear site energies.

Abstract

The modified discrete nonlinear Schr\"odinger equation is used to study the formation of stationary localized states in a one-dimensional lattice with a single impurity and an asymmetric dimer impurity. A periodically modulated and a perfectly nonlinear chain is also considered. Phase diagrams of localized states for all systems are presented. From the mean square displacement calculation, it is found that all states are not localized even though the system comprises random nonlinear site energies. Stability of the states is discussed.