SELF-SIMILAR SOLUTIONS FOR A GENERALIZED NONLINEAR SCHRODINGER EQUATION WITH HIGHER-ORDER VARYING DISPERSIONS AND NONLINEARITIES

In this paper, a generalized nonlinear Schrodinger equation with varying second-, third-, fourth-, fifth-, and sixth-order dispersions, cubic-quintic-septic nonlinearity, and gain/loss is investigated. By means of the similarity transformation, exact self-similar soliton solutions, including bright and dark soliton solutions, are constructed. Based on the exact soliton solutions, we study the corresponding propagation dynamics in a periodically modulated fiber system. The results show that in the absence of gain/loss, the soliton solutions exhibit a periodic oscillatory evolution behavior, and with the periodic modulation of the gain/loss, the dark soliton switch can be implemented. Finally, the stability of the self-similar solutions against the constraint deviations and the initial perturbations are also investigated by employing direct numerical simulations.