DCDS-S
Periodic solutions of inhomogeneous Schrödinger flows into 2-sphere
Ping-Liang Huang Youde Wang
In this paper,we consider the so called generalized inhomogeneous Schrödinger flows from a closed Riemann surface $M$ into the standard 2-sphere $S^2$ associated with the energy functional given by \begin{align*} E_{f,P}(u)=\int_M\left(\frac{1}{2}f|\nabla u|^2+P(u_3)\right)dV_g. \end{align*} We showed the existence of special periodic solutions to the generalized inhomogeneous Schrödinger flows from $M$ with convolution symmetry (especially $M = S^2$) into $S^2$ when the function $f$ and $P$ satisfy certain conditions respectively. Especially, we show that the inhomogeneous Heisenberg spin chain system from a closed Riemann surface with convolution symmetry admits some special periodic solutions if the coupling function $f$ satisfies some suitable conditions. We also prove that there exist an infinite number of special periodic solutions to the Landau-Lifshitz system with an external magnetic field from $S^2$ into $S^2$.
keywords: convolution symmtry. special periodic solution $S^1$-invariant inhomogeneous Heisenberg spin chain system Schrödinger flow

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