Journal of East China Normal University(Natural Sc ›› 2017, Vol. 2017 ›› Issue (6): 50-62.doi: 10.3969/j.issn.1000-5641.2017.06.005

• Mathematics • Previous Articles     Next Articles

Symmetry reductions, exact solutions and conservation laws of a class of forth-order partial differential equations

ZHANG Li-xiang, LIU Han-ze, XIN Xiang-peng   

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng Shandong 252059, China
  • Received:2016-12-14 Online:2017-11-25 Published:2017-11-25

Abstract: The partial differential equation with constant coefficients can merely approximately reflect the law of motion of substances. Relatively the partial differential equation with variable coefficients can reflect the complex movement of substances more accurately. Therefore, it is more important to study the partial differential equations with variable coefficients. This paper investigates a class of variable coefficient partial differential equations. By using Lie symmetry analysis, the symmetries of the equations are obtained, Then the partial differential equations are reduced to ordinary differential equations. Moreover, we combine with (G'/G) expansion method and elliptic function expansion, so exact solutions to the original equation are obtained. Furthermore, the conservation laws of this kind of variable coefficient differential equations are given.

Key words: variable coefficient equation, Lie symmetry analysis, exact solution, conservation law

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