What are the key differences between linear and non-linear waves?

[quid]

Could someone please tell me the fundamental differences between linear and non-linear waves?

 

[toombs]

Usually, linear means if f(x, t) and g(x, t) are both solutions, then so is Af + g. I think though sometimes in the context of wave mechanics and optics "linear" just means non-dispersive. Can I get some backup on that? Non-dispersive meaning the wave speed is not a function of wavelength and phase speed equals group speed. It is possible to have a linear equation that produces dispersive waves. Example: the free particle Schrödinger equation: $-\frac{\hbar^2}{2m} \psi_{xx} = i\hbar \psi_t$

 

[quid]

Right, Thanks toombs

 

[Bobbywhy]

Here is a comprehensive discussion of both linear and nonlinear waves:

http://www.scholarpedia.org/article/Linear_and_nonlinear_waves