Physical and dynamic characteristics of high-amplitude ultrasonic wave propagation in nonlinear and dissipative media

This study presents a comprehensive investigation into the soliton solutions for the Khokhlov–Zabolotskaya–Kuznetsov ([Formula: see text]) problem using the Bernoulli sub-equation function approach, generalized Kudryashov method, and Homotopy perturbation method. The [Formula: see text] equation, a nonlinear wave equation that governs the propagation of high-amplitude ultrasonic waves through nonlinear media, is studied in detail. Perturbation theory and asymptotic expansions are employed to derive approximate solutions for the [Formula: see text] problem. These methodologies offer valuable insights into the behavior of ultrasonic waves in different media, thereby facilitating the optimization of ultrasonic transducer design and enhancing the precision of ultrasonic imaging systems. The analytical and semi-analytical methods utilized for solving the [Formula: see text] equation are computationally efficient and serve as valuable resources for researchers and engineers working in the field of ultrasonics. The outcomes of this study carry significant implications for the understanding of ultrasonic wave behavior in nonlinear and dissipative media, ultimately contributing to the development of more accurate and efficient ultrasonic imaging techniques.