_{1}

In this work, we propose a model of oscillation of Davydov solitons in three wells. It can be used as a mathematical and physical frame in simulation of circle of some nonlinear oscillation of excitations via acupuncture system. The calculation shows that this sort of oscillation is possible if the initial rate of average occupational number of the quasi-particles in the wells is not equal to zero. One of oscillations arising relies on the initial rate of average occupational number of quasi-particles to be equal with each other within three wells. Then, the oscillation is not a kind of Josephson oscillation and has complicated frequency distributions. However, the total behavior of oscillation played is similar to three big solitons concentrated in three wells. In this sense, this model generally reveals a sort of oscillation mechanism of the acupuncture system how to work in the body, which allows us to understand the oscillation that may be one of fundamental natures in the acupuncture system.

Bio-excitations interaction with living organization of our body appears many non- linear effects, which is a significant issue studied in biophysics, bio-photonics, or even life sciences [^{−1}, with amide-I exciton infrared absorption spectra observed on the 1666 cm^{−1} line, which demonstrates that there is a red shift of 16 cm^{−1} corresponding to the formation of just soliton bound energy. However, Davydov soliton seems to appear that short time span is serious obstacle to explain why it is a basic unit of energy and information transmission in bio-systems. For improving this weakness of the model, many scholars proposed modified models [

In this work, we propose a model of oscillation of the Davydov solitons, via an acupuncture system (so called medial vein), in three wells of potentials to simulate the Davydov solitons condensation in three areas of living system. The author hopes this studying is constructive to allow us understand that there may exist three condensations of solitons restricted in three areas in human body, which may provide a possible mechanism to explain working nature of three acupuncture points, i.e. upper, middle and lower Dantian as described by Chinese medicine and acupuncture theory [

Let us consider a Davydov bio-vibration system in our body which is described by a nonlinear Schrödinger equation [

where g is a coupling number, the wave function

where

By instead Equation (2) into Equation (1), we obtain

which can describe oscillation of soliton in three wells, where the relevant parameters are defined by

and

Then through observation, the solution for Equation (4) can be approximately constructed by

Then replacing Equation (8) into Equation (4), we can get

This gives

and

The first Equation (10) can be simplified as

where the physical meaning of

here

where

here the conditions

On the other hand, for solving the second Equation (11) it is obviously to have

and

Therefore, we eventually obtain the solution

This shows that the oscillation posesses complicated frequency distributions and therefore it is not a Josephson oscillation as

pying quasi-particle numbers for the oscillation

then the total oscillation will take part in three big solitons confined in three wells, respectively, which are described by Equation (19).

In conclusions, the above model can be used in simulation of circle of some nonlinear excitations moving in the acupuncture system in advanced level, such as meaning of qi (here can be understood that the Davydov solitons is a kind of qi) moving in the medial vein and oscillation in three Dantians. The calculation shows that this sort of oscillation is possible if the initial rate of average occupational number of the quasi-particles in the wells is not equal to zero. One of simple oscillations arising relies on the initial rate of average occupational number of quasi-particles to be equal with each other within three wells, then the oscillation is not a kind of Josephson oscillation and has complicated frequency distributions, however the total behavior of oscillation played is similar to three big solitons concentrated in three wells. In the same way, the model of oscillation can be extended to oscillation over three wells system, such as oscillation in seven wells, to mimic working function of complicated medial vein + circle system which is also described by the theory of ancient Indian Yoga. In this sense, this model generally reveals a sort of oscillation mechanism of acupuncture system to working in our body, and explains clearly what means oscillation of qi, i.e. oscillation of Davydov solitons. This allows us to propose an assumption: there is no clear bio-structure (in the level of anthropotomy) and only has functional structure for acupuncture system. The oscillation of various excitatoins [

Qiao, B. (2016) Oscillation of Davydov Solitons in Three Wells. Journal of Modern Physics, 7, 1811- 1817. http://dx.doi.org/10.4236/jmp.2016.713161