1/2 t)]-

Evolution equations for the coefficients A1 and A2 on the various time scales 71, 7 2 , ... , are found by asymptotic analysis. They have the form

( 41)

where Di,1 and Di,2 are polynomials of degree i. In addition, there is an equation forB,

( 42)

The analytical procedure that leads to the dynamical system is complicated in one sense, but straightforward in another. It is complicated because it involves the solution of inhomogeneous boundary value problems, which become more and more involved as one goes to higher-order time scales. What is particularly annoying is that the evolution on the lower-order scales is usually trivial, i.e., A1 and A2 do not depend on 7 1 and possibly higher-order 7i, and one does not know a priori how high one has to go in the asymptotic analysis before one finds a nontrivial dynamical system. On the other hand, the procedure is straightforward in the sense that there is an algorithm that outlines the process in a step-by-step manner and that is guaranteed to be finite in length if the problem is set up correctly.