Stationary localized states due to quadratic nonlinearity in one dimensional systems

TL;DR

This paper studies how quadratic nonlinear impurities influence the formation and stability of stationary localized states in one-dimensional systems, providing new insights into nonlinear impurity effects.

Contribution

It introduces a comprehensive analysis of stationary localized states caused by quadratic nonlinear impurities and explores their stability in various nonlinear configurations.

Findings

Quadratic nonlinear impurities can induce localized states in 1D systems.

Stability of states is related to their energy, shown graphically.

Stationary localized states are also formed in fully nonlinear systems with uniform nonlinear strengths.

Abstract

We investigate the effect of a nondegenerate quadratic nonlinear dimeric impurity on the formation of stationary localized states in one dimensional systems. We also consider the formation of stationary localized states in a fully nonlinear system where alternative sites have same nonlinear strengths. Appropriate ansatzs have been chosen for all the cases which reproduce known results for special cases. Connection of the stability of a state with its energy is presented graphically.