Abel Hill Inverse Problem for Two Non-Monotonic Cases

Authors

  • Eric Kincanon Gonzaga University, Spokane WA USA

DOI:

https://doi.org/10.14419/9f1kfh23

Published

25-03-2026

Keywords:

Abel’s Hill; Inverse Problems; Monotonic Functions

Abstract

Abel’s Hill as an inverse problem has been solved for piecewise monotonic potentials. This brief paper considers two cases which ‎extend this solution. These cases correspond to the extreme possibilities for the potential’s slope, zero and infinite. The effect on the meas‎ured return times are discussed and it is found that it is straightforward to identify potentials with these characteristics.

References

N. H. Abel, Resolution d'un probleme de mecanique, J. Reine Angew. Math., 1 (1826) 13-18.

M. Razavy, An Introduction to Inverse Problems in Physics, World Scientific, (2020), pp:6-15. https://doi.org/10.1142/11860.

J.B. Keller, Inverse Problems, Am. Math. Monthly, 83 (1976) 107-118. https://doi.org/10.1080/00029890.1976.11994053.

E. Hecht, Physics 3rd ed., Brooks/Cole, (2001), pp: 35-80

How to Cite

Kincanon, E. (2026). Abel Hill Inverse Problem for Two Non-Monotonic Cases. International Journal of Applied Mathematical Research, 15(1), 31-33. https://doi.org/10.14419/9f1kfh23

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