Mixed-type soliton solutions for the NN-coupled Hirota system in an optical fiber

Under investigation in this paper is the NN-coupled Hirota system which describes the ultrashort pulse simultaneous propagation of the NN-field components in an optical fiber. Through the Hirota method and symbolic computation, using some auxiliary functions, we obtain the improved bilinear forms and two mixed-type soliton solutions for the 33-coupled Hirota system, while the system admits two mixed-type solitons for all the cases of σ1σ1, σ2σ2 and σ3σ3, which the represent the defocusing or focusing nonlinearities of the 33 components. With the help the analytic and graphic analysis, we study the properties and interactions for the two mixed-type solitons for the 33-coupled Hirota system. Amplitudes for the two mixed-type one solitons are not affected by γγ, but their velocities are linearly related to γγ, with γγ as the higher-order effect which represents the relative width of the spectrum that arises due to the quasi-monochromocity. For the 2-bright-1-dark two solitons, there exist the elastic and inelastic interactions, while for the 1-bright-2-dark two solitons, there is only the elastic interaction. The 2-bright-1-dark and 1-bright-2-dark bound-state two solitons are also presented. Finally, we extend those results to the NN-coupled Hirota system.