Revisiting Separation of Variables in Hamilton-Jacobi Equations: Conclusion, Statements and More

Table of Links

Abstract and Introduction

Conclusion, Statements and Declarations, and Bibliography

Conclusion

Summarising, we believe that the statement made in the papers [1, 2] about new scientific results in the problem of complete separation of variables in the HamiltonJacobi equation for geodesics does not correspond to reality. We did not find any new results in comparison with those contained in the theorem on necessary and sufficient conditions of Vladimir N. Shapovalov. The results of the article in question, unlike the original ones, have omissions, and the article contains incorrect statements. Thus, the methods and results proposed in the works [1, 2] do not contain scientific novelty and represent a special case of the theory of complete separation of variables in the free Hamilton-Jacobi equation, finally constructed in the 70s of the last century.

Statements and Declarations

Data availability statement

All necessary data and references to external sources are contained in the text of the manuscript. All information sources used in the work are publicly available and refer to open publications in scientific journals and textbooks.

Compliance with Ethical Standards

The authors declare no conflict of interest.

Bibliography

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