Geometry and nonlinear evolution equations |
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Authors: | Radha Balakrishnan |
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Institution: | (1) The Institute of Mathematical Sciences, 600 113 Madras, India |
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Abstract: | We briefly review the nonlinear dynamics of diverse physical systems which can be described in terms of moving curves and
surfaces. The interesting connections that exist between the underlying differential geometry of these systems and the corresponding
nonlinear partial differential equations are highlighted by considering classic examples such as the motion of a vortex filament
in a fluid and the dynamics of a spin chain. The association of the dynamics of a non-stretching curve with a hierarchy of
completely integrable soliton-supporting equations is discussed. The application of the surface embeddability approach is
shown to be useful in obtaining such connections as well as exact solutions of some nonlinear systems such as the Belavin-Polyakov
equation and the inhomogeneous Heisenberg chain. |
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Keywords: | Nonlinear dynamics geometry |
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