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\begin{document}

\title{Lie group approach for constructing all reciprocal transformations. The
two-dimensional stationary gas dynamics equations}



\author[1]{Piyanuch Siriwat}%
\author[2]{Sergey Meleshko}%
\affil[1]{ Mae Fah Luang University, Chiang Rai, 57100, Thailand}%
\affil[2]{SUT}%


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  \date{June 18, 2024}


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\begin{abstract}
Recently, an infinitesimal approach for finding reciprocal
transformations has been proposed. The method uses the group analysis
approach and consists of similar steps as for finding an equivalence
group of transformations. The new method provides a systematic tool for
finding classes of reciprocal transformations (group of reciprocal
transformations). Similar to the classical group analysis this approach
can be also applied for finding all reciprocal transformations (not only
composing a group) of the equations under study. The present paper
provides this algorithm. As an illustration, the method is applied to
the two-dimensional stationary gas dynamics equations. Equivalence
group, group of reciprocal transformations and completeness of all
discrete reciprocal transformations are presented in the paper. The
results are stated in form of a theorem.%
\end{abstract}%



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