Analysis of Solitary Waves in Arteries

Solitary waves are coincided with separaterices, which surrounds an equilibrium point with characteristics like a center, a sink, or a source. The existence of closed or spiral orbits in phase plane predicts the existence of such an equilibrium point. If there exists another saddle point near that equilibrium point, separatrix orbit appears. In order to prove the existence of solution for any kind of boundary value problem, we need to apply a fixed-point theorem. We have used the Schauder’s fixed-point theorem to show that there exists at least one nontrivial solution for equation of wave motion in arteries, which has a spiral characteristic. The equation of wave motion in arteries has a nonlinear character. Thus, the amplitude of the wave depends on the wave velocity. There is no general analytical or straightforward method for prediction of the amplitude of the solitary wave. Therefore, it must be found by numerical or nonstraightforward methods. We introduce and analyse three methods: saddle point trajectory, escape moving time, and escape moving energy. We apply these methods and show that the results of them are in agreement, and the amplitude of a solitary wave is predictable.