Recently by using path integral method and theory of soliton, a new calcula
tion scheme of a partition function of an immersion object has been propose
d [J. Phys. A 31 (1998) 2705-2725]. In this paper, the scheme to elastica (
space curve with the Bernoulli-Euler functional) immersed in three-dimensio
nal space [R-3 as a physical model in polymer science is applied. It is sho
wn that the nonlinear Schrodinger and complex modified Korteweg-de Vries hi
erarchies naturally appear to express the functional space of the partition
function. In other words, it is shown that the configuration space of an e
lastica immersed in R-3 can be classified by these equations. Then the part
ition function is reduced to an ordinary integral over the orbit space of t
hese hierarchies. (C) 1999 Elsevier Science B.V. All rights reserved.