  We use the reduction of the string dynamics on R_t x S^3 to the
Neumann-Rosochatius integrable system to map all string solutions described by
this dynamical system onto solutions of the complex sine-Gordon integrable
model. This mapping relates the parameters in the solutions on both sides of
the correspondence. In the framework of this approach, we find finite-size
string solutions, their images in the (complex) sine-Gordon system, and the
leading finite-size effects of the single spike "E-\Delta\phi" relation for
both R_t x S^2 and R_t x S^3 cases.
