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Schwarzian derivative in higher-order Riccati equations

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Abstract

The Sturm–Liouville equation represents the linearised form of the first-order Riccati equation. This provides an evidence for the connection between Schwarzian derivative and this first-order nonlinear differential equation. Similar connection is not obvious for higher-order equations in the Riccati chain because the corresponding linear equations are of order greater than two. With special attention to the second- and third-order Riccati equations we demonstrate that Schwarzian derivative has a natural space in higher Riccati equations. There exist higher-order analogues of the Schwarzian derivative. We demonstrate that equations in the Riccati hierarchy are embedded in these higher-order derivatives.

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Acknowledgements

One of the authors (GAS) would like to acknowledge funding from the Science and Engineering Research Board, Govt. of India through Grant No. CRG/2019/000737.

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Authors and Affiliations

  1. Department of Physics, Visva-Bharati University, Santiniketan, 731235, India

    Benoy Talukdar

  2. Department of Physics, Bidhannagar College, EB-2, Sector-1, Salt Lake, Kolkata, 700064, India

    Supriya Chatterjee

  3. Department of Physics, Kazi Nazrul University, Asansol, 713303, India

    Golam Ali Sekh

Authors
  1. Benoy Talukdar
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  2. Supriya Chatterjee
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  3. Golam Ali Sekh
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Correspondence to Golam Ali Sekh.

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Talukdar, B., Chatterjee, S. & Sekh, G.A. Schwarzian derivative in higher-order Riccati equations. Pramana - J Phys 97, 187 (2023). https://doi.org/10.1007/s12043-023-02681-3

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  • DOI: https://doi.org/10.1007/s12043-023-02681-3

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