PTsymmetric nonlinear optical lattice: Analytical solutions

Localized and periodic solutions for the nonlinear Schrödinger equation with spatially modulated nonlinearity are found. A linear stability analysis corroborated by direct numerical simulation reveals that the regions of stability of these solutions can be controlled by tuning the values of real and imaginary parts of the linear refractive index modulation profile as well as by tuning the real part of nonlinearly modulated spatial distribution. In particular, the role played by the competing gain and loss parameter as well as by the parameter of periodic spatial distribution towards the magnitude of the stability domains is reported.