Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (1): 24-31.doi: 10.3969/j.issn.1000-5641.2019.01.003

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Lie symmetry analysis, Bäcklund transformation and exact solutions for a class of fourth-order partial differential equations

DAI Hui-ju, LI Lian-zhong, WANG Qi, SHA An   

  1. School of Science, Jiangnan University, Wuxi Jiangsu 214122, China
  • Received:2017-09-20 Online:2019-01-25 Published:2019-01-24

Abstract: This paper investigates a class of variable coefficient partial differential equations. By using the homogeneous balance method, the Bäcklund transformation is obtained, which leads to exact solutions for the equation. By applying Lie symmetry analysis, the symmetries and vector field of the equation are obtained. Then, by means of a similarity transformation, the partial differential equations are reduced to ordinary differential equations. Solving the reduced equations, we investigate the exact solutions to the equations concisely using the power series expansion method.

Key words: Bäcklund transformation, fourth-order partial differential equation, Lie symmetry analysis, power series expansion method, exact solution

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