Do linear AND dispersive waves exist outside of QM?

[LarryS]

Outside of QM, do perfectly linear waves really exist in nature? I am referring to just those waves that also have dispersion - in which the wave components have differing phase velocities.

... or are we just using the mathematics of linear systems to approximate nonlinear systems?

Thanks in advance.

 

[jasonRF]

Interesting question.

All of the classical waves in dispersive media I can think of are described by fundamentally nonlinear models.

One case that I initially thought might work are waves in structures. Consider electromagnetic waves in a waveguide. If the waveguide is an ideal perfect conductor and is in perfect vaccuum, then you get linear dispersive waves. The problem of course occurs if you need the waveguide to be made with a real material. At the very least, the surface fields and currents on that material cannot become arbitrarily large before catastrophic changes to the material occur; milder (but important) nonlinearities probably occur before then, anyway.

Of course, there are many instances where the linearized approximation is very good, just like there are some where the nonlinearities are very important.

Jason