PDE from dispersion relation?

Suppose I have knowledge of a system's dispersion relation $f(\omega,k)$. Is it possible to recover the underlying PDE describing the system? Can I simply use the replacement $k=-i\nabla$, $\omega=i\frac{d}{dt}$ to go back?I came across one source which claimed that the original PDE could only be recovered to a certain extent. An example given was the Dirac and Klein Gordon equations which both satisfy the same dispersion relation. But I didn't quite follow. Example: I have a polynomial dispersion relation of the form $\omega^2+c^2k^2=1$. Can I...Read more

Dispersion through Glass Slab

My questions related Dispersion through Glass Slab: Why does a parallel surface makes a difference?Why is that light do get disperse in a prism and a glass slab at surface one but at backs normal at the surface of slab but not at surface of prism? Answer:Problem with that solution is even if the slab is made up of two glass prism why should there be two ($3$ in total) bending of light. As the slab is continuous, will there be no change in speed of light inside the glass slab?Thus shouldn't slab too behave like prism?...Read more

Dispersion between analog and digital signal in optical fiber

We know that optical fiber is used to transmit data in digital format.As a result, there is either Intermodal or Intramodal dispersion occurring based on the fiber used for communication. If an analog signal is used to transmit the data what happens to the signal. Does it undergo dispersion? How is the dispersion of analog signal different from digital one....Read more

dispersion - Why do we need coefficient of mean deviation?

Mean deviation can give us a sense of how much data is dispersed from one of the average measurements (mean,mode,median). Mean deviation depends on the difference between the data and the average measurement.$MD=1/n∑(x - y)$ where x is the different data values and y is the mean/mode/median.I don't think it really depends on the average. Rather it is completely controlled by the data differences from the average value. What I thought at first is maybe we need the $Coefficient$ $of$ $mean$ $deviation$ to compare two or more data lists. But when ...Read more