We use the reduction of the string dynamics on Rt × 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 − ∆ϕ ” relation for both Rt × S 2 and Rt × S 3 cases. On leave from Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences
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