EFFECTS OF PERIODICALLY-MODULATED THIRD-ORDER DISPERSION ON PERIODIC SOLUTIONS OF NONLINEAR SCHRODINGER EQUATION WITH COMPLEX POTENTIAL

We study, both analytically and numerically, families of periodic solutions of the nonlinear Schrodinger equation with periodically-modulated third-order dispersion (TOD) and complex-valued potential. The TOD and the complex potential are built as solutions of an inverse problem, which predicts the explicit expressions of the complex-valued potential and the TOD supporting a required phase-gradient structure of the periodic solutions. We investigate in detail the band structure of the stability problem of the periodic solutions in the corresponding periodic complex potential by means of plane-wave-expansion method and direct numerical simulations of the evolution of the perturbed inputs. The results show that the band stability domains of the periodic solutions may be narrowed when increasing the nonlinear effects and the amplitudes of periodic solutions.