Stationary localized states in one-dimensional systems due to modified nonlinear impurities

Discrete nonlinear Schrödinger equation (DNLS) of the form ${i(dC}_n{/dt)=C}_{n+1\mathrm{}}{+C}_{n-1}-{\chi }_n(|C_{n+1\mathrm{}}{|}^2+|C_{n-1}{|}^2-2|C_n{|}^2{)C}_n$ 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 stability of the states and its connection with the nonlinear strength is presented. Results are compared with those obtained from other DNLS’s. It is found that the DNLS used in this paper has more impact on the formation of stationary localized states.