SYMMETRY ANALYSIS, CONSERVATION LAWS OF A TIME FRACTIONAL FIFTH-ORDER SAWADA-KOTERA EQUATION

Zheng Xiao; Long Wei

doi:10.11948/2017078

2017 Volume 7 Issue 4

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Zheng Xiao, Long Wei. SYMMETRY ANALYSIS, CONSERVATION LAWS OF A TIME FRACTIONAL FIFTH-ORDER SAWADA-KOTERA EQUATION[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1275-1284. doi: 10.11948/2017078

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Zheng Xiao, Long Wei. SYMMETRY ANALYSIS, CONSERVATION LAWS OF A TIME FRACTIONAL FIFTH-ORDER SAWADA-KOTERA EQUATION[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1275-1284. doi: 10.11948/2017078

SYMMETRY ANALYSIS, CONSERVATION LAWS OF A TIME FRACTIONAL FIFTH-ORDER SAWADA-KOTERA EQUATION

Department of Mathematics, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, China

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Abstract

Abstract

In this paper, we intend to study the symmetry properties and conservation laws of a time fractional fifth-order Sawada-Kotera (S-K) equation with Riemann-Liouville derivative. Applying the well-known Lie symmetry method, we analysis the symmetry properties of the equation. Based on this, we find that the S-K equation can be reduced to a fractional ordinary differential equation with Erdelyi-Kober derivative by the similarity variable and transformation. Furthermore, we construct some conservation laws for the SK equation using the idea in the Ibragimov theorem on conservation laws and the fractional generalization of the Noether operators.
- S-K equation /
- Lie symmetry /
- conservation laws
MSC: 58J70;45K05;35Q53

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References

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