  We study a family of classical string solutions with large spins on R x S^3
subspace of AdS_5 x S^5 background, which are related to Complex sine-Gordon
solitons via Pohlmeyer's reduction. The equations of motion for the classical
strings are cast into Lame equations and Complex sine-Gordon equations. We
solve them under periodic boundary conditions, and obtain analytic profiles for
the closed strings. They interpolate two kinds of known rigid configurations
with two spins: on one hand, they reduce to folded or circular
spinning/rotating strings in the limit where a soliton velocity goes to zero,
while on the other hand, the dyonic giant magnons are reproduced in the limit
where the period of a kink-array goes to infinity.
