Localized waves for the mixed coupled Hirota equations in an optical fiber

Abstract

Under investigation in this paper are the mixed coupled Hirota equations, which describe the simultaneous propagation of two ultrashort optical fields in an optical fiber. With respect to the two-component electric fields in the fiber, we construct the Lax pair, Nth-order Darboux transformation, and two types of the first-order and second-order localized wave solutions are derived. Based on such solutions, moving breathers, Akhmediev breathers, multi-peak solitons and anti-dark solitons are obtained. We find that the increase of the strength of the higher-order linear/nonlinear effects leads to the decrease of the velocity of the moving breather. Breather-to-soliton conversion is studied. We show that the moving breather can be converted to the anti-dark soliton. Elastic interactions between the breathers and dark solitons are studied. Additionally, inelastic interaction between the anti-dark soliton and dark soliton is shown.