Rogue wave solutions to the coupled Sasa–Satsuma equation

Abstract

In this paper, general rogue wave solutions to the coupled Sasa–Satsuma (CSS) equation are constructed by the Kadomtsev–Petviashvili (KP) reduction method. These rogue wave solutions are classified into three families, which correspond to one complex simple root, two complex simple roots, and one complex double root of an octic algebraic equation related to the dimension reduction condition, respectively. All of these complex roots should have nonzero real and imaginary parts. Furthermore, by considering the case where either only real roots or both real and complex roots of the aforementioned octic algebraic equation are present, other rational solutions such as W-shaped soliton and the mixture of W-shaped soliton and rogue wave solutions to the CSS equation are derived and illustrated.