Solitons, kink-solitons and breather solutions of the two-coupled incoherent nonlinear Schrödinger equation

In this paper, we attain the analytical soliton solutions for the two-coupled incoherent nonlinear Schrödinger equation via the Hirota bilinear method, and this equation is always used to describe the pulse propagation in high birefringent fibers. We also select different relevant parameters to construct different types of solutions including multiple-soliton, two-kink-soliton and breather solutions, which is an important tool to investigate the influence of these related parameters with different function types on solitons propagations and interactions. It is worth noting that the multiple-soliton solutions obtained are bright–dark alternating, which is not seen in previous literature. At the same time, in order to better understand the physical significances of all kinds of solutions, the 3D images are drawn with different shapes and parameters. Finally, the dynamic behaviors for two-soliton solutions before and after collision are also discussed by asymptotic analysis.