Dark Soliton and Breather Solutions to the Coupled Sasa–Satsuma Equation

We construct dark soliton and breather solutions to the coupled Sasa–Satsuma (CSS) equation under nonzero boundary condition. First, the CSS equation is bilinearized into six equations by introducing three auxiliary tau functions. Then, it is shown that these six bilinear equations can be reduced from a set of 33 bilinear equations in the Kadomtsev–Petviashvili (KP)-Toda hierarchy including the discrete KP equation. As a result, two alternative determinant forms of the dark soliton and breather solutions, along with their mixed type, are derived. The rich structures and the dynamical behaviors of both dark and breather solutions are analyzed and illustrated. Especially, the resonant breather and resonant dark soliton solutions are found in the same determinant form.