Soliton Solutions to the Coupled Sasa‐Satsuma‐mKdV Equation

ABSTRACT We consider the soliton solutions of a recently proposed coupled Sasa‐Satsuma‐modified Korteweg‐de Vries (Sasa‐Satsuma‐mKdV) equation using the Kadomtsev–Petviashvili reduction method. Under zero, nonzero and mixed boundary conditions, we derive four distinct classes of soliton solutions: bright–bright, dark–dark, bright–dark, and dark–bright. These solutions are derived from the vector Hirota equation, for which the bright, dark, and bright–dark soliton solutions are provided in the Appendix. We perform asymptotic analysis of soliton collisions for each class of solutions. Inelastic collisions are observed between bright–bright solitons. In the dark–dark case, the soliton structures are similar to those of the Sasa‐Satsuma equation which include double‐hole, Mexican hat and anti‐Mexican hat solutions. The collision between these solitons and kink solitons and the resonances between dark–dark solitons and breather–breather are new phenomena found in the coupled Sasa‐Satsuma‐mKdV equation.