Merge pull request #2915 from ArnoStrouwen/docs

rewrite nonlinear solve tutorial

Author: ChrisRackauckas

docs/src/tutorials/nonlinear.md

@@ -1,10 +1,18 @@
 # Modeling Nonlinear Systems
 
-In this example, we will go one step deeper and showcase the direct function
-generation capabilities in ModelingToolkit.jl to build nonlinear systems.
-Let's say we wanted to solve for the steady state of an ODE. This steady state
-is reached when the nonlinear system of differential equations equals zero.
-We use (unknown) variables for our nonlinear system.
+ModelingToolkit.jl is not only useful for generating initial value problems (`ODEProblem`).
+The package can also build nonlinear systems.
+This is, for example, useful for finding the steady state of an ODE.
+This steady state is reached when the nonlinear system of differential equations equals zero.
+
+!!! note
+    
+    The high level `@mtkmodel` macro used in the
+    [getting started tutorial](@ref getting_started)
+    is not yet compatible with `NonlinearSystem`.
+    We thus have to use a lower level interface to define nonlinear systems.
+    For an introduction to this interface, read the
+    [programmatically generating ODESystems tutorial](@ref programmatically).
 
 ```@example nonlinear
 using ModelingToolkit, NonlinearSolve
@@ -15,8 +23,6 @@ using ModelingToolkit, NonlinearSolve
 eqs = [0 ~ σ * (y - x)
        0 ~ x * (ρ - z) - y
        0 ~ x * y - β * z]
-guesses = [x => 1.0, y => 0.0, z => 0.0]
-ps = [σ => 10.0, ρ => 26.0, β => 8 / 3]
 @mtkbuild ns = NonlinearSystem(eqs)
 
 guesses = [x => 1.0, y => 0.0, z => 0.0]
@@ -26,7 +32,9 @@ prob = NonlinearProblem(ns, guesses, ps)
 sol = solve(prob, NewtonRaphson())
 ```
 
-We can similarly ask to generate the `NonlinearProblem` with the analytical
+We found the `x`, `y` and `z` for which the right hand sides of `eqs` are all equal to zero.
+
+Just like with `ODEProblem`s we can generate the `NonlinearProblem` with its analytical
 Jacobian function:
 
 ```@example nonlinear