The fractional nonlinear impurity: A Green function approach

We use a lattice Green function approach to study the stationary modes of linear/nonlinear (Kerr) impurity embedded in periodic one-dimensional where we replace standard discrete Laplacian by fractional one. The energies and mode profiles are computed closed form, for different exponents strengths. lie outside linear band whose bandwidth decreases steadily as exponent decreases. For any values, there is always single bound state while nonlinear case, up two states possible, strengths above certain threshold. energy (or that upper one), becomes directly proportional strength at large transmission plane waves also form several exponents, various observe fractionality tends increase overall transmission. selftrapping transition shifts lower nonlinearity values decreased. In both cases, nonlinear, trapping zero strength, which can be explained near-degeneracy spectrum limit small exponent.