Existence and uniqueness of the solution to the modified Schrödinger map

We prove the local existence of the solution to a certain system of nonlinear Schrödinger equations arising from Schrödinger maps for the initial data in $H^{s}(\mathbf{R}^{2})$ with $s >1/2$. The uniqueness of the solution is also proved when the data belong to $H^{1}(\mathbf{R}^{2})$.

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Published 1 January 2005