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Journal of Vibration Testing and System Dynamics 7(1) (2023) 49--58 | DOI:10.5890/JVTSD.2023.03.007

P.~Siriwat$^1$, S. V. Meleshko$^2$

$^1$ School of Science, Mae Fah Luang University, Chiang Rai, 57100, Thailand

$^2$ School of Mathematics, Institute of Science, Suranaree University of Technology, 30000, Thailand

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Abstract

A new method for constructing reciprocal transformations is proposed. The method uses the same steps as for finding equivalence group of transformations. It provides a systematic tool for finding classes of reciprocal transformations. As an illustration the method is applied to the one-dimensional gas dynamics equations, and new reciprocal transformations are found.

Acknowledgments

We are very thankful to Professor Colin Rogers for attracting my attention to reciprocal transformations. The research of SVM was supported by the Russian Science Foundation Grant No. 18-11-00238 'Hydrodynamics-type equation: symmetries, conservation laws, invariant difference schemes'.

References

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