Lie symmetry analysis, traveling wave solutions and conservation laws of a Zabolotskaya-Khokholov dynamical model in plasma physics

This article analyzes the analytic and solitary wave solutions of the one-dimensional Zabolotskaya-Khokholov (ZK) dynamical model which provides information about the propagation of sound beam or confined wave beam in nonlinear media and studies of beam deformation. By the Lie symmetry analysis method, we acquire the vector fields, commutation relations, optimal system, reduction, and analytic solutions to the specified equation by exerting the Lie group method. Moreover, the solitary wave solutions of the ZK model are procured by exerting the new auxiliary equation method (NAEM). The behavior of the acquired outcomes for several cases is exhibited graphically through two and three-dimensional dynamical wave profiles. Furthermore, the conservation laws of the ZK model are acquired by Ibragimov’s new conservation theorem. • This article analyzes the one-dimensional Zabolotskaya-Khokholov dynamical model. • The Lie symmetry analysis is performed on the mentioned model. • Moreover, the solitary wave solutions of the ZK model are procured by exerting the new auxiliary equation method. • The conservation laws are also discussed. • These findings demonstrate the novelty of our strategy and offer strong support for the efficacy and reliability of our methodology.