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In this paper we study the existence of special symmetric solutions to aHamiltonian hyperbolic-hyperbolic coupled spin-field system, where the spinsare maps from $\mathbb R^{2+1}$ into the sphere $\S^2$ or the pseudo-sphere$\H^2$. This model was introduced in \cite{Martina} and it is also known as the{\it hyperbolic-hyperbolic generalized Ishimori system}. Relying on thehyperbolic coordinates introduced in \cite{KNZ11}, we prove the existence ofequivariant standing waves in both regular hyperbolic coordinates as well assimilarity variables, and describe their asymptotic behaviour.

Equivariant and self-similar standing waves for a Hamiltonian hyperbolic-hyperbolic spin-field system