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In this paper, we give the N-fold Darboux transformation (DT) for the continuous Heisenberg spin chain which describes the motion of the isotropic ferromagnets in the complex case. By using this DT, we get N-soliton solutions and a new exact solution of the spin chain from a trivial seed solution and a plane wave seed solution, respectively.

Darboux Transformation and Exact Solutions of the Continuous Heisenberg Spin Chain Equation