loading page

Lie group approach for constructing all reciprocal transformations. The two-dimensional stationary gas dynamics equations
  • Piyanuch Siriwat,
  • Sergey Meleshko
Piyanuch Siriwat
Mae Fah Luang University, Chiang Rai, 57100, Thailand

Corresponding Author:[email protected]

Author Profile
Sergey Meleshko
Author Profile


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.
13 Mar 2022Submitted to Mathematical Methods in the Applied Sciences
14 Mar 2022Assigned to Editor
14 Mar 2022Submission Checks Completed
29 Mar 2022Reviewer(s) Assigned
12 Jul 2022Review(s) Completed, Editorial Evaluation Pending
23 Jul 2022Editorial Decision: Accept
03 Aug 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8614