Abel Hill Inverse Problem for Two Non-Monotonic Cases

  • Authors

    • Eric Kincanon Gonzaga University, Spokane WA USA
    https://doi.org/10.14419/9f1kfh23

    Received date: February 10, 2026

    Accepted date: March 20, 2026

    Published date: March 25, 2026

  • 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

    1. N. H. Abel, Resolution d'un probleme de mecanique, J. Reine Angew. Math., 1 (1826) 13-18.
    2. M. Razavy, An Introduction to Inverse Problems in Physics, World Scientific, (2020), pp:6-15. https://doi.org/10.1142/11860.
    3. J.B. Keller, Inverse Problems, Am. Math. Monthly, 83 (1976) 107-118. https://doi.org/10.1080/00029890.1976.11994053.
    4. E. Hecht, Physics 3rd ed., Brooks/Cole, (2001), pp: 35-80

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  • 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