Is this PDE linear or non-linear?

[Ein Krieger]

hello, guys
Below is the equation I am concerned with:

Is the above equation non-linear because of (delta P/delta x)^2 term assuming other variables are constant and don't change with pressure , P?

 

[HallsofIvy]

It is non-linear because of, as you say, that $\left[\partial p/\partial x\right]^2$

 

[Ein Krieger]

Ok.
What kind of method can you suggest to deal with [∂p/∂x] 2 ?

I am going to convert the above equation to ODE by method of lines in Matlab. I guess that non-linear terms require special approach.