Insights into acoustic beams in nonlinear, weakly dispersive and dissipative media

This study examines the (2+1)–dimensional dissipative Zabolotskaya–Khokhlov equation, a fundamental nonlinear wave model with broad applications in diverse physical domains, such as acoustic wave propagation, nonlinear optics, and fluid dynamics. This equation exhibits profound connections with other nonlinear evolution equations, particularly in describing wave interactions in dispersive and dissipative media, highlighting its significance in characterizing complex wave phenomena. The principal objective of this work is to derive both closed-form and numerical solutions to gain deeper insight into the equation’s underlying dynamics. To this end, we employ the Khater II and the modified Kudryashov approaches-two systematic mathematical techniques for obtaining explicit solutions. Additionally, He’s variational iteration method is implemented as a numerical scheme to evaluate the reliability and precision of the derived exact solutions. A comparative assessment of the analytical and numerical results underscores the accuracy of the obtained solutions and the effectiveness of the employed methods in handling highly nonlinear wave systems. This investigation provides novel perspectives on dissipative wave dynamics and illustrates the advantages of integrating exact and numerical methodologies. The findings hold substantial implications for applications in fluid mechanics, nonlinear optics, and acoustic wave theory, fostering a more comprehensive understanding of nonlinear dissipative structures.