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We analyse several physical aspects of the dressed elliptic stringspropagating on $\mathbb{R} \times \mathrm{S}^2$ and of their counterparts inthe Pohlmeyer reduced theory, i.e. the sine-Gordon equation. The solutions aredivided into two wide classes; kinks which propagate on top of ellipticbackgrounds and those which are non-localised periodic disturbances of thelatter. The former class of solutions obey a specific equation of state that isin principle experimentally verifiable in systems which realize the sine-Gordonequation. Among both of these classes, there appears to be a particular classof interest the closed dressed strings. They in turn form four distinctsubclasses of solutions. Unlike the closed elliptic strings, these foursubclasses, exhibit interactions among their spikes. These interactionspreserve a carefully defined turning number, which can be associated to thetopological charge of the sine-Gordon counterpart. One particular class ofthose closed dressed strings realizes instabilities of the seed ellipticsolutions. The existence of such solutions depends on whether a superluminalkink with a specific velocity can propagate on the corresponding ellipticsine-Gordon solution. Finally, the dispersion relations of the dressed stringsare studied. A qualitative difference between the two wide classes of dressedstrings is discovered. This would be an interesting subject for investigationin the dual field theory.

Salient Features of Dressed Elliptic String Solutions on $\mathbb{R}\times$S$^2$