Investigation of Stationary Localized States Caused by a Nonlinear Dimer in a One-Dimensional Chain

This work investigates the emergence of stationary localized states induced by a nonlinear dimer embedded in a one-dimensional discrete linear chain. Using the discrete nonlinear Schrödinger (DNLS) framework, we explore the influence of nonlinearity on localization, bifurcation, and symmetry breaking. Analytical expressions for stationary modes are derived using an exponential decay ansatz, and the results are validated through numerical simulations. The study demonstrates that above a critical nonlinearity threshold, the system exhibits self-trapping and a transition from symmetric to asymmetric localized modes, represented by a pitchfork bifurcation. The findings provide a clear understanding of energy confinement and symmetry breaking in discrete nonlinear systems relevant to optical lattices, molecular chains, and condensed matter systems.