I have this PDE : $\displaystyle \frac{ \partial^4 v}{\partial t^4}=kv\left(\frac{\partial^2 m}{\partial n^2}\right)^2$
and I wanna understand what's the reason it is non-linear PDE. I have some information about lineality when we have only one dependind function "u(x,t)" for example but in this case we have two depending variables...
I suppose the second partial differential term is not linear due it has a square power but what about variable "v"; it is a depending variable also, so I am wondering if it could affect the lineality of the PDE too?
thanks for your help.