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We investigate the dynamical behavior of finite rings of classical spinvectors interacting via nearest-neighbor isotropic exchange in an externalmagnetic field. Our approach is to utilize the solutions of a continuum versionof the discrete spin equations of motion (EOM) which we derive by assumingcontinuous modulations of spin wave solutions of the EOM for discrete spins.This continuous EOM reduces to the Landau-Lifshitz equation in a particularlimiting regime. The usefulness of the continuum EOM is demonstrated by thefact that the time-evolved numerical solutions of the discrete spin EOM closelytrack the corresponding time-evolved solutions of the continuum equation. Ofspecial interest, our continuum EOM possesses soliton solutions, and we findthat these characteristics are also exhibited by the corresponding solutions ofthe discrete EOM. The robustness of solitons is demonstrated by consideringcases where initial states are truncated versions of soliton states and bynumerical simulations of the discrete EOM equations when the spins are coupledto a heat bath at finite temperatures.

Modulated spin waves and robust quasi-solitons in classical Heisenberg rings