Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations

Journal of Inequalities and Applications

Jianming Qi¹  Yongyi Gu² 

[1] Department of Mathematics and Physics, Shanghai Dianji University;School of Mathematics and Information Science, Guangzhou University;

关键词: nonlinear evolution equations;    symmetry;    exp ( − ϕ ( z ) ) $\exp(-\phi(z))$ -expansion method;    complex method;    exact solutions;    meromorphic function;   

DOI  :  10.1186/s13660-017-1587-5

来源: DOAJ

【 摘 要 】

Abstract In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the exp ( − ϕ ( z ) ) $\exp(-\phi (z))$ -expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

【 授权许可】

Unknown