A BASIS OF HIERARCHY OF GENERALIZED SYMMETRIES AND THEIR CONSERVATION LAWS FOR THE (3+1)-DIMENSIONAL DIFFUSION EQUATIONA

Jean Juste Harrisson Bashingwa; Abdul Kara

doi:10.11948/20190360

2020 Volume 10 Issue 5

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Jean Juste Harrisson Bashingwa, Abdul Kara. A BASIS OF HIERARCHY OF GENERALIZED SYMMETRIES AND THEIR CONSERVATION LAWS FOR THE (3+1)-DIMENSIONAL DIFFUSION EQUATIONA[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 2163-2183. doi: 10.11948/20190360

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Jean Juste Harrisson Bashingwa, Abdul Kara. A BASIS OF HIERARCHY OF GENERALIZED SYMMETRIES AND THEIR CONSERVATION LAWS FOR THE (3+1)-DIMENSIONAL DIFFUSION EQUATIONA[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 2163-2183. doi: 10.11948/20190360

A BASIS OF HIERARCHY OF GENERALIZED SYMMETRIES AND THEIR CONSERVATION LAWS FOR THE (3+1)-DIMENSIONAL DIFFUSION EQUATIONA

Jean Juste Harrisson Bashingwa^1, ,,
Abdul Kara²

1.
C B Division, University of Cape Town, Anzio Road, 7785, South Africa
2.
School of Mathematics, Faculty of Science, University of the Witwatersrand, South Africa

Corresponding author: Jean Juste Harrisson Bashingwa. Email: jean.bashingwa@uct.ac.za(J. Bashingwa)

Abstract

Abstract

We determine, by hierarchy, dependencies between higher order linear symmetries which occur when generating them using recursion operators. Thus, we deduce a formula which gives the number of independent generalized symmetries (basis) of several orders. We construct a basis for conservation laws (with respect to the group admitted by the system of differential equations) and hence generate infinitely many conservation laws in each equivalence class.
- Recursion operators /
- generalized symmetries /
- conservation laws
MSC: 47F05, 51P05

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References

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