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has been cited by the following article:

• TITLE: The Prolongation Structures for the System of the Reaction-Diffusion Type

  AUTHORS: Xiaojuan Duan

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.1, January 24, 2017

  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.