Localized states due to the coupling of exciton with the coupled lattice oscillators

TL;DR

This paper investigates the formation and stability of localized states in a one-dimensional nonlinear lattice modeled by a discrete nonlinear Schrödinger equation, emphasizing the influence of nonlinear impurities and comparing with other models.

Contribution

It introduces a specific form of DNLS to analyze localized states due to nonlinear impurities, highlighting its greater impact compared to other models.

Findings

Localized states depend on nonlinear impurity strength.

Stability of states varies with nonlinear parameters.

The model shows enhanced localization effects.

Abstract

Discrete nonlinear Schr\"oginger equation (DNLS) of the form, $i \frac{dC_n} {dt}$ = $C_{n+1}$ + $C_{n-1}$ - $ \chi_n [|C_{n+1}|^2 + |C_{n-1}|^2 - 2 |C_n|^2] C_n$ is used to study the formation of stationary localized states in one dimensional system due to a single as well as a dimeric nonlinear impurity. The fully nonlinear chain is also considered. The stability of the states and its connection with the nonlinear strength is presented. Results are compared with those obtained from other DNLS. It is found that the DNLS used in this paper has more impact in the formation of stationary localized states.