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The harmonic map is introduced and several physical applications are presented. The classical nonlinear σ model can be looked at as the embedding of a two-dimensional surface in a threedimensional sphere, which is itself embedded in a four-dimensional space. A system of nonlinear evolution equations are obtained by working out the zero curvature condition for the Gauss equations relevant to this geometric formulation.

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Copyright Info: © 2016, Paul Bracken, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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