Reply to Professor Yehia comments arXiv:1305.0026

This is a reply to Professor Yehia Comments in arXiv:1305.0026

💡 Research Summary

This document is a formal rebuttal by G. Valent to the comments made by Professor H. M. Yehia in arXiv:1305.0026. Yehia alleged that Valent’s two recent papers—one on integrable systems with a cubic first integral (Commun. Math. Phys. 299 (2010) 631) and another on systems with a quartic first integral (arXiv:1304.5859v1)—failed to cite Yehia’s earlier work properly and, moreover, contained no original contributions beyond what Yehia had already published. Valent systematically refutes these claims by outlining the novel aspects of each paper and clarifying the citation record.

In the first paper, Valent derives an explicit closed‑form expression for a class of integrable systems characterized by a cubic first integral. The derivation occupies three pages, after which fifteen pages are devoted to a global analysis: determining the parameter ranges for which the system is defined on a smooth manifold, describing the topology of that manifold, and establishing global invariants. Yehia’s earlier articles (