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The Prolongation Structures for the System of the Reaction-Diffusion Type

DOI: 10.4236/jamp.2017.51010, PP. 92-100

Keywords: Prolongation Structure, Reaction-Diffusion, Realization, Abelian Covering

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Abstract:

Equations of the reaction-diffusion type are very well known and have been extensively studied in many research areas. In this paper, the prolongation structures for the system of the reaction-diffusion type are investigated from theory of coverings. The realizations and the classifications of the one-dimensional coverings of the system are researched. And the corresponding conservation law of the one-dimensional Abelian coverings is concluded, which is closely connected with the symmetry of the system by Noether theorem.

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