The extended tanh method for new compact and noncompact solutions for the KP–BBM and the ZK–BBM equations

This paper is devoted to studying the KP–BBM and the ZK–BBM equations. The extended tanh method is used to conduct the analysis. The KP–BBM and the ZK–BBM equations give rise to compactons solutions: solitons with the absence of infinite tails, solitons: nonlinear localized waves of infinite support, solitary patterns solutions having infinite slopes or cusps, and plane periodic solutions. The work confirms the power of the proposed method.