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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.


Copyright 2016, Paul Bracken, licensee AIMS Press.

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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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AIMS Mathematics



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Mathematics Commons



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