Desai and Lieber 



n-l 



'1 ^"m 2 





fin- 



^n-1 ^n-l^^^n-l V 2_ ^ 



n > 1 



"~* Br r 3^ r ^^ , ^ 



- n = 1 



1 , + + n > 1 



""1 Br •■ dt) "" 



n > 



m = <^6^ _; _ _ 



7 



n-l 



ban- E F^^V. V. n >0 



n-l 



El 3 

 ^ n > 



d, =7"-- — 4j n>0 



(1.34) 



fan - " n = 1 



l^^n-1 ^^Vn-1 l^V^n-l ^^Vn-l 



= - — n > 1 . 



r 3(9 Br ^ Br Bt? 



From Eqs. (1.30a), (1.31a), and (1.32a) we see that the groups are so 

 formed that, for n > 0, the n-th group involves only the linear terms in u^, v^ 

 and their derivatives with coefficients aj,,, bj^, etc., depending on Uj, v^ and 

 their derivatives i=l, 2, ..., n-l. For n = o, the group involves non- 

 linear terms in u^, v^ and their derivatives. We could have arranged the 

 terms so that this group for n = also involved only the linear terms in uq, vq 

 and their derivatives by transferring the nonlinear terms to the n = i group so 

 that 



536 



