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

doi:10.3969/j.issn.1000-5641.2017.06.005

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ZHANG Li-xiang, LIU Han-ze, XIN Xiang-peng. Symmetry reductions, exact solutions and conservation laws of a class of forth-order partial differential equations[J]. Journal of East China Normal University (Natural Sciences), 2017, (6): 50-62. doi: 10.3969/j.issn.1000-5641.2017.06.005

Citation:

ZHANG Li-xiang, LIU Han-ze, XIN Xiang-peng. Symmetry reductions, exact solutions and conservation laws of a class of forth-order partial differential equations[J]. Journal of East China Normal University (Natural Sciences), 2017, (6): 50-62. doi: 10.3969/j.issn.1000-5641.2017.06.005

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

doi: 10.3969/j.issn.1000-5641.2017.06.005

School of Mathematical Sciences, Liaocheng University, Liaocheng Shandong 252059, China

Received Date: 2016-12-14
Publish Date: 2017-11-25

Abstract

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.
- variable coefficient equation,
- Lie symmetry analysis,
- exact solution,
- conservation law

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References(22)

References

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