Soliton solution and bifurcation analysis of the Zakharov–Kuznetsov–Benjamin–Bona–Mahoney equation with power law nonlinearity

This paper addresses the Zakharov–Kuznetsov–Benjamin–Bona–Mahoney equation with power law nonlinearity. First the soliton solution is obtained by the aid of traveling wave hypothesis and along with it the constraint conditions fall out naturally, in order for the soliton solution to exist. Subsequently, the bifurcation analysis of this equation is carried out and the fixed points are obtained. The phase portraits are also analyzed for the existence of other solutions.

► The traveling wave solution of the ZK–BBM equation with arbitrary power law nonlinearity is obtained.
► The bifurcation analysis is carried out.
► Several other solutions are retrieved, including the singular solitary waves.