Periodic waves and optical solitons in a novel resonant third-order nonlinear Schrödinger equation

The existence of a rich variety of periodic and localized waves is demonstrated for an optical fiber system described by a new resonant third-order nonlinear Schrödinger equation. The derived nonlinear waves include solutions incorporating the Weierstrass function, periodic solutions, soliton solutions, and doubly periodic solutions. The newly found structures are derived by utilizing four integration approaches, namely the Weierstrass elliptic function expansion method, the Weierstrass semi-rational expansion technique, the extended Jacobi elliptic function expansion methodology, and the modified Jacobi elliptic function expansion approach. Based on a similarity transformation between the generalized resonant third-order nonlinear Schrödinger equation with variable coefficients and the related constant coefficient one, we construct the analytical nonautonomous bright and dark soliton solutions for the variable coefficient model. As an application, we discuss the evolutional dynamics of the recovered nonautonomous solitons in a periodically modulated fiber system. The results show that the dynamical behavior of nonautonomous solitons can be effectively controlled through a proper choice of the third-order dispersion and gain/loss parameters.