LAUSR

Abstract Optical fibers are used in the optical sensing and optical fiber communication. In this paper, we investigate a variable-coefficient coupled Hirota system which describes the vector optical pulses in an inhomogeneous optical fiber. With respect to the complex wave envelopes, we construct the one-fold solutions which describe the two breather-like solitons and one breather, and two-fold solutions which describe the four breather-like solitons and two breathers. We obtain the one- and two-fold breather-to-soliton conversion conditions which are both related to α ( z ) and β ( z ) , the coefficients of the group velocity dispersion and third-order dispersion. Based on the one-fold breather-to-soliton conversion condition, we present several types of the nonlinear waves and the corresponding relations on α ( z ) and β ( z ) . Interaction between the Akhmediev breather/Kuznetsov-Ma breather and breather-like soliton is shown. Maximum amplitudes of the Akhmediev breather/Kuznetsov-Ma breather and breather-like soliton are related to δ ( z ) , where δ ( z ) denotes the coefficient of the nonlinear terms corresponding to the self-phase modulation and cross-phase modulation. When α ( z ) and β ( z ) meet the one-fold breather-to-soliton conversion condition, interaction between the periodic wave/anti-dark/multi-peak/ M -shaped soliton and breather-like soliton is presented. Interaction between the two-Kuznetsov-Ma breather and two-breather-like soliton is shown. Maximum amplitudes of the two-Kuznetsov-Ma breather and two-breather-like soliton are related to δ ( z ) . When α ( z ) and β ( z ) meet the two-fold breather-to-soliton conversion conditions, interaction between the two-anti-dark and two-breather-like soliton is shown.