Symmetry analysis and conservation laws of the modified Korteweg–de Vries equation with a quartic nonlinear term

Journal of Taibah University for Science

Gangwei Wang¹  Zhijun Wang¹  Guosheng Tang² 

[1] Hebei University of Economics and Business;Jiangsu University of Science and Technology;

关键词: modified korteweg–de vries equation with a quartic nonlinear term;    symmetries;    symmetry reduction;    exact solutions;    conservation laws;   

DOI  :  10.1080/16583655.2022.2032546

来源: DOAJ

【 摘 要 】

In this paper, a modified Korteweg–de Vries equation with a quartic nonlinear term in two-electron temperature plasmas is studied. Firstly, the symmetries are constructed using the generalized symmetry method. In addition, the potential equation is studied, it can been found that this equation does not posses potential symmetries. Meanwhile, the symmetry reduction and group-invariant solutions are derived rely on the one-dimensional optimal system of subalgebras. Finally, conservation laws are showed resort by the multipliers method, three polynomial type conserved quantities are presented, also the Hamiltonian form is obtained. In particular, reciprocal Bäcklund transformations for conservation laws are obtained for the first time.

【 授权许可】

Unknown