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.
Paul Bracken. Harmonic Maps Surfaces and Relativistic Strings[J]. AIMS Mathematics, 2016, 1(1): 1-8. doi: 10.3934/Math.2016.1.1
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