Darboux transformation of a two‐component generalized Sasa–Satsuma equation and explicit solutions

Under investigation in this paper is a two‐component generalized Sasa–Satsuma equation associated with a 4 × 4 matrix spectral problem. We construct Darboux transformation for the two‐component generalized Sasa–Satsuma equation on basis of the gauge transformation between the Lax pairs. The corresponding N ‐fold Darboux transformation is derived in terms of both iterative representation and compact determinant form. As applications of the Darboux transformation together with the limit technique, some interesting solutions including traveling soliton solutions, breather soliton solutions, and rogue wave solutions are explicitly obtained and graphically illustrated.