Bilinear Forms and Dark-Dark Solitons for the Coupled Cubic-Quintic Nonlinear Schrödinger Equations with Variable Coefficients in a Twin-Core Optical Fiber or Non-Kerr Medium**Supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11805020, 11272023 and 11471050, the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05),

Abstract

Twin-core optical fibers are applied in such fields as the optical sensing and optical communication, and propagation of the pulses, Gauss beams and laser beams in the non-Kerr media is reported. Studied in this paper are the coupled cubic-quintic nonlinear Schrödinger equations with variable coefficients, which describe the effects of quintic nonlinearity for the ultrashort optical pulse propagation in a twin-core optical fiber or non-Kerr medium. Based on the integrable conditions, bilinear forms are derived, and dark-dark soliton solutions can be constructed in terms of the Gramian via the Kadomtsev-Petviashvili hierarchy reduction. Propagation and interaction of the dark-dark solitons are presented and discussed through the graphic analysis. With different values of the delayed nonlinear response effect b(z), where z represents direction of the propagation, the linear- and parabolic-shaped one dark-dark soltions can be derived. Interactions between the parabolic- and periodic-shaped two dark-dark solitons are presented with b(z) as the linear and periodic functions, respectively. Directions of velocities of the two dark-dark solitons vary with z and the amplitudes of the solitons remain unchanged can be observed. Interactions between the two dark-dark solitons of different types are displayed, and we observe that the velocity of one soliton is zero and direction of the velocity of the other soliton vary with z. We find that those interactions are elastic.