Painlevé property, nonlocal symmetry and interaction waves in a (2+1)-dimensional extended KP–Benjamin–Ono equation

Abstract This paper focuses on the analytical technique based on nonlocal symmetry and consistent tanh expansion method for constructing abundant analytical solutions of a new extended Kadomtsev–Petviashvili–Benjamin–Ono (eKP–BO) equation in (2+1) dimensions. First, commencing with the Painlevé analysis, the integrability of the (2+1)-dimensional eKP–BO equation and its nonlocal symmetry are discussed. Second, the localization of the nonlocal symmetry of the extended system is determined by means of the prolongation method. Furthermore, through this localization process, the initial value problem of the extended system is solved, thereby providing a finite symmetry transformation of the (2+1)-dimensional eKP–BO equation. Finally, we follow the consistent tanh expansion method to unveil the interaction solutions of the soliton-cnoidal type and resonant soliton type to the eKP–BO equation, and we study their dynamic properties in a visual manner.