Close to the Giant Magnons

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We consider the most general string configurations on the Rₜ x S³ subspace of AdS₅ xS⁵, described by the Neumann-Rosochatius integrable system. Under some restrictions on the parameters of the solution and in an appropriate limit, they correspond to small deviation from the known finite-size giant magnon solutions with one and two angular momenta. Analyzing the finite-size effect on the dispersion relation, we find that the leading correction is modified in a way similar to the gamma-deformed case Rₜ x S³gamma. The subleading correction for a string with one angular momentum is also found. It depends on the same parameter, which describes the generalization of the leading correction.