Constructing various wave symmetries on the blood flow and arterial wall motion model using the Hirota bilinear method

In this research, the Hirota bilinear method is used for the development and examination of different types of wave symmetries of a blood flow and arterial wall motion model. Understanding such wave propagation is essential for modeling cardiovascular dynamics and diagnosing vascular disorders. Various ansatz functions were adopted, such as interaction via two exponents, M-shaped interaction with one kink, M-shaped interaction with two kinks, mixed waves, multi-waves, periodic lump waves, periodic cross kink waves, and homoclinic breather waves. This study produced solutions in various forms: including dark soliton, M-shaped waves, periodic structures, and localized waveforms such as lumps and breather solutions. These solutions reveal complex nonlinear behaviors such as phase shifts, localized waveforms, and interference patterns. The construction and visualization of these solutions are obtained with the support of Mathematica. Three-dimensional (3D) surfaces, contours, and two-dimensional (2D) plots provide good insights into the propagation, stability, and interactions of the waves. These results enhance our understanding of pulse wave dynamics in elastic arteries and demonstrate the robustness of the bilinear method for physiological modeling. It shows how effective this approach is in modeling complex waveforms and thus in enhancing the understanding of cardiovascular waves. This work employs the Hirota bilinear framework to classify standard and degenerate waveforms, including new configurations not previously reported in this model.