Some previous articles have consistently formulated the open states in
deoxyribonucleic acid (DNA) and synthetic polynucleotide double helic
es as coupled sine-Gordon equations. But the solutions of the equation
s have not been obtained for general cases. In this paper, that is don
e by applying a function transformation. The method leads to a superpo
sition relation cos[1/2(phi+phi')] = C cos[1/2 (phi-phi')], for C = co
nst, which gives the soliton couples, the helix-kink couples and so on
. Some interesting properties are treated in detail and the applicatio
ns of these properties in the dynamics of real B-DNA are discussed.