Abstract
More and more researches evidence that hemodynamic factors play an important role in the occurrence and development of cardiovascular diseases. In this paper, a new mathematical model has been proposed to describe rogue waves in arterial vessels. Based on two‐dimensional Navier–Stokes (NS) equation and continuity equation, vorticity equation satisfied by blood flow is given. Further, by employing multiscale analysis and perturbation expansion method, the ( )‐dimensional nonlinear Schrödinger (NLS) equation is derived to describe the envelope solitary waves propagation of blood vessels. Different from the previous model, the ( )‐dimensional NLS model takes into account the propagation of blood flow along the vessel axis and radius. In order to further study, the integer‐order model is generalized to the time‐fractional nonlinear Schrödinger (TF‐NLS) equation by use of the semi‐inverse method and Agrawal's method, and the conservation laws are also investigated. Moreover, the rogue wave solution of the fractional model which can directly describe the behavior of the rogue waves in arterial vessels is obtained. Rogue wave and fractional parameter effect on blood flow volume is analyzed and discussed, which can provide some help for the study of cardiovascular diseases.
Published Version
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