Nonlinear surface impurity in a semi-infinite 2D square lattice

Details Nonlinear surface impurity in a semi-infinite 2D square lattice Nonlinear surface impurity in a semi-infinite 2D square lattice

2006-04-24

arxiv.org/abs/nlin/0604060v1

Phys. Rev. B 74, 045412 (2006)

Nonlinear Sciences

Pattern Formation and Solitons

6 pages, 7 figures, submitted to PRB

Scientific paper

10.1103/PhysRevB.74.045412

We examine the formation of localized states on a generalized nonlinear impurity located at, or near the surface of a semi-infinite 2D square lattice. Using the formalism of lattice Green functions, we obtain in closed form the number of bound states as well as their energies and probability profiles, for different nonlinearity parameter values and nonlinearity exponents, at different distances from the surface. We specialize to two cases: impurity close to an "edge" and impurity close to a "corner". We find that, unlike the case of a 1D semi-infinite lattice, in 2D, the presence of the surface helps the formation of a localized state.

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