A Perspective on Classical Strings from Complex Sine-Gordon Solitons

We study a family of classical string solutions with large spins on Rt×S subspace of AdS5×S background. These solutions are related to Complex sine-Gordon solitons via Pohlmeyer’s reduction. The equations of motion for the classical strings are cast into Lamé 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.