Darboux-dressing transformation, semi-rational solutions, breathers and modulation instability for the cubic-quintic nonlinear Schrödinger system with variable coefficients in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide

Abstract

Abstract Twin-core optical fibers are applied in the fiber optic sensing technique and optical communication. Non-Kerr media are seen in plasma physics, nonlinear quantum mechanics and nonlinear optics. Propagation of an optical beam and superradiance for an atom in the waveguide are reported. This paper investigates the cubic-quintic nonlinear Schrödinger system with variable coefficients for the ultrashort optical pulse propagation in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide. For the two components of the electromagnetic fields, Darboux-dressing transformation, semi-rational solutions and breather solutions are obtained. We acquire the Akhmediev breathers (ABs) and Kuznetsov-Ma (KM) solitons. Interaction between the rogue waves and KM/bright-dark solitons is presented. When b(z) is a linear/quadratic/cosine function, the ABs, rogue waves, KM and bright-dark solitons appear parabolic, cubic and wavy, respectively, where b(z) presents the delayed nonlinear response effects. We conduct the modulation instability for the plane wave solutions for a non-Kerr medium, twin-core nonlinear optical fiber or waveguide via the linear stability analysis: If χ < 0, the solutions are modulationally stable; otherwise, modulationally unstable, where χ is the growth rate of the instability.