Diversity of solitonic wave structures to the M‐truncated dynamical system in ultrasound imaging

Abstract

The utilization of ultrasound imaging has become extensively prevalent and well‐established in clinical practice. The fundamental technologies that serve as the foundation for various applications in the field include transducers, beam shaping, pulse compression, tissue harmonic imaging, contrast agents, methodologies for quantifying blood flow and tissue motion, and three‐dimensional imaging. This article focuses on the examination of ultrasonic propagation, which involves the transmission of mechanical vibrations within the molecules or particles of a material. It quantifies the velocity of sound propagation in the medium of air. The third‐order nonlinear M‐fractional Westervelt model has been used as a governing model in the imaging process for securing the different wave structures. The recently developed computational methods have been applied in this study. The different wave structures are secured in various forms of solitary wave solutions including bright, dark, and combo solitons. In the domains of medical imaging and therapy, the investigation of sound wave propagation and high‐amplitude phenomena is facilitated by the utilization of wave structures. The effectiveness of these solutions extends to acoustic cavitation, acoustic levitation, underwater acoustics, and facilitating the process of ultrasonic propagation in tissue. Ultrasound imaging technologies currently find application in the medical field, enabling the visualization and examination of internal human tissue. This technology exhibits a wide array of applications in the fields of industry and medicine. A representation of the graphs is produced using the appropriate parametric values. The results suggest that the chosen approaches exhibit effectiveness, viability, and adaptability when implemented in complex systems in various fields, with particular emphasis on ultrasonic imaging.