A novel (2+1)-dimensional complex coupled dispersionless system: Darboux transformation and multisolitons

Abstract This study presents a (2+1)-dimensional complex coupled dispersionless system. A Lax pair is proposed, and the Darboux transformation is employed to construct multisoliton solutions. These solutions exhibit a range of wave phenomena, including bright and dark solitons, S-shaped formations, parabolic profiles, and periodic wave patterns. Additionally, it is shown that the system is equivalent to the sine-Gordon equation and the negative flow of the modified Korteweg–de Vries hierarchy through appropriate transformations.