Equivariant and self-similar standing waves for a Hamiltonian hyperbolic-hyperbolic spin-field system
arXiv:1309.5066
Abstract
In this paper we study the existence of special symmetric solutions to a Hamiltonian hyperbolic-hyperbolic coupled spin-field system, where the spins are maps from into the sphere 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 the hyperbolic coordinates introduced in \cite{KNZ11}, we prove the existence of equivariant standing waves in both regular hyperbolic coordinates as well as similarity variables, and describe their asymptotic behaviour.
Expanded Introduction. To appear in SIAM Journal of Math. Analysis (SIMA)