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

作者: Xiaojuan Duan

DOI: 10.4236/JAMP.2017.51010

关键词:

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

参考文章(13)
V. V. Lychagin, A. M. Vinogradov, I. S. Krasilʹshchik, Geometry of jet spaces and nonlinear partial differential equations Gordon and Breach Science Publishers. ,(1986)
Wei-Zhong Zhao, Min-Li Li, Yu-Hai Qi, Ke Wu, Modified Heisenberg Ferromagnet Model and Integrable Equation Communications in Theoretical Physics. ,vol. 44, pp. 415- 418 ,(2005) , 10.1088/6102/44/3/415
V Grassi, G Profilo, E Alfinito, G Soliani, R A Leo, Equations of the reaction-diffusion type with a loop algebra structure Inverse Problems. ,vol. 14, pp. 1387- 1401 ,(1998) , 10.1088/0266-5611/14/6/003
Qiusheng CHENG, Jingsong HE, The Prolongation Structures and Nonlocal Symmetries for Modified Boussinesq System Acta Mathematica Scientia. ,vol. 34, pp. 215- 227 ,(2014) , 10.1016/S0252-9602(13)60139-3
I. S. Krasil’shchik, A. M. Verbovetsky, R. Vitolo, A Unified Approach to Computation of Integrable Structures Acta Applicandae Mathematicae. ,vol. 120, pp. 199- 218 ,(2012) , 10.1007/S10440-012-9699-X
Xiao-Juan Duan, Ming Deng, Wei-Zhong Zhao, Ke Wu, The prolongation structure of the inhomogeneous equation of the reaction-diffusion type Journal of Physics A. ,vol. 40, pp. 3831- 3837 ,(2007) , 10.1088/1751-8113/40/14/006
Qing Ding, Jun-ichi Inoguchi, Schrödinger flows, binormal motion for curves and the second AKNS-hierarchies Chaos Solitons & Fractals. ,vol. 21, pp. 669- 677 ,(2004) , 10.1016/J.CHAOS.2003.12.092
A. M. Vinogradov, Local symmetries and conservation laws Acta Applicandae Mathematicae. ,vol. 2, pp. 21- 78 ,(1984) , 10.1007/BF01405491
F. B. Estabrook, H. D. Wahlquist, Prolongation structures of nonlinear evolution equations. II Journal of Mathematical Physics. ,vol. 17, pp. 1293- 1297 ,(1976) , 10.1063/1.523056
I. S. Krasilshchik, A. M. Vinogradov, Nonlocal symmetries and the theory of coverings: An addendum to A. M. vinogradov's ‘local symmetries and conservation laws” Acta Applicandae Mathematicae. ,vol. 2, pp. 79- 96 ,(1984) , 10.1007/BF01405492