u  =  a x;
ϵ  =  (∂_x) 
          u  +  (1/2) (∂_x) u (∂_x) u

e  =  (∂_x) u

f  = e/ϵ // Simplify

s  = Evaluate[Solve[f == 0.9, a]]

e  /.  s
ϵ  /.  s