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arXiv · 1309.5066

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

Nan Lu·Andrea Nahmod·Chongchun Zeng
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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 $\mathbb R^{2+1}$ into the sphere $§^2$ 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 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.

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Nan Lu, Andrea Nahmod, Chongchun Zeng. 2014-10-20. Equivariant and self-similar standing waves for a Hamiltonian hyperbolic-hyperbolic spin-field system. https://arxiv.org/abs/1309.5066

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