Analytical and computational evaluation of a Navier-Stokes-type model revealed diverse wave behaviors, including Jacobi elliptic and chaotic regimes, governed by system parameters in elastic vessels.
The study provides novel exact solutions and dynamical insights into nonlinear wave propagation in biological dispersive media using a Navier-Stokes-type model.
ABSTRACT This study investigates a nonlinear evolution model derived from the Navier‐Stokes equations to describe wave propagation in elastic cylindrical vessels. The interplay between dispersive and nonlinear effects is crucial in blood flow dynamics, leading to wave deformation, interactions, and complex propagation patterns in biological fluid systems. Within this framework, the governing nonlinear model is analytically examined, and a novel class of exact wave solutions is constructed using the Bäcklund transformation and the ‐expansion method. These approaches generate a wide spectrum of solutions, including Jacobi elliptic, trigonometric, hyperbolic, and rational wave structures. The obtained solutions reveal diverse wave behaviors governed by system parameters and provide deeper physical insight into nonlinear propagation mechanisms. To further explore the model's dynamical features, bifurcation and chaos analyses are performed. Bifurcation diagrams are employed to identify transitions between steady, periodic, and complex regimes, while the presence of chaotic behavior and its sensitivity to key system parameters are systematically investigated. In addition, the effects of parameter variations on wave amplitude, velocity, and profile characteristics are analyzed. Graphical visualizations are presented to illustrate the evolution of wave structures under varying parameter values. The results enrich the spectrum of exact solutions for Navier‐Stokes‐type models and contribute to a better understanding of nonlinear wave dynamics in biological dispersive media.
Majid et al. (Mon,) conducted a other in Blood flow dynamics in elastic cylindrical vessels. Analytical and computational modeling was evaluated on Wave propagation behaviors, exact solutions, and dynamical features. Analytical and computational evaluation of a Navier-Stokes-type model revealed diverse wave behaviors, including Jacobi elliptic and chaotic regimes, governed by system parameters in elastic vessels.