Nonconstant Limit
Suppose that
. In this limit, Equation (5.78) reduces to

(5.99) 
In the various nonconstant regimes considered in Section 5.11, the previous equation takes the form

(5.100) 
where is real and nonnegative, and is a complex constant. Let . The previous equation
yields

(5.101) 
This equation is identical in form to Equation (5.88), which we have already solved. Indeed, the solution that
is bounded as
has the small expansion (5.90), where
,
, and
. Matching to Equation (5.83) yields

(5.102) 
The layer width in space again scales as
. This width must be
less that . As before, the neglect of the term involving in Equation (5.74) is
justified provided that
.