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 self-localized states in a translationally invariant fully nonlinear system where alternative sites have the same nonlinear strengths. Appropriate ansatze have been chosen for all of the cases which reproduce the known results for special cases. The connection of the stability of a state to its energy is presented graphically.
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