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Simulation of Minimal Surfaces by Isovector Methods
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| Transactions of the Society for Computer Simulation |
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The non-linear minimal surface equation is expressed as an ideal of differential forms. The isovector fields of the ideal are constructed using its transport property under Lie derivatives. The corresponding orbital equations generate an invariant group of transformations which serves two objectives. First, it enables one to construct new solutions from the known solutions of the minimal surface equation, and secondly it reduces the minimal surface equation to a non-linear ordinary differential equation. For a particular choice of parameters, exact solutions are obtained and 3D-graphs of some minimal surfaces are depicted using the Mathematica software package.
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