Abstract
In this study, the abundant families of nonlinear acoustic wave structures are constructed for Zabolotskaya-Khokholov (Z-K) model which provides information about the propagation of sound beam or confined wave beam in nonlinear media and studies of beam deformation. These wave structures are observed in single (shock and singular) and mixed shock, (complex solitary-shock, shock-singular and periodic-singular) forms. The rational solutions are also emerged during the derivation. The new modified extended direct algebraic (NMEDA) technique and mathematics software are used to obtain the solutions. Moreover, for different values of parameters, the graphs in 3D and 2D-dimensions are also drawn. (c) 2022 Elsevier B.V. All rights reserved.