Stationary localized states due to a nonlinear dimeric impurity embedded in a perfect one-dimensional chain

Abstract

The formation of stationary localized states due to a power law nonlinear dimeric impurity embedded in a perfect one-dimensional chain is studied here using the appropriate discrete nonlinear Schr\"odinger equation. A proper ansatz is introduced in the appropriate Hamiltonian to obtain the reduced effective Hamiltonian. The Hamiltonian contains a parameter, \ensuremath{\mathrm{B}}=${\mathrm{\ensuremath{\varphi}}}_{1}$/${\mathrm{\ensuremath{\varphi}}}_{0}$, which is the ratio of stationary amplitudes at impurity sites. Relevant equations for localized states are obtained from the fixed point of the reduced dynamical system. The complete phase diagram in the (\ensuremath{\chi},\ensuremath{\sigma}) plane for all permissible values of |\ensuremath{\mathrm{B}}|\ensuremath{\leqslant}1 is obtained. Furthermore, the maximum number of localized states is found to be 6.