Schwarzian derivative in higher-order Riccati equations

被引：0
作者：
Benoy Talukdar
Supriya Chatterjee
Golam Ali Sekh
机构：
[1] Visva-Bharati University,Department of Physics
[2] Bidhannagar College,Department of Physics
[3] Kazi Nazrul University,Department of Physics
来源：
Pramana | / 97卷
关键词：
higher-order Riccati equations; linearised form; Schwarzian derivative; higher-order analogue; 02.30.Jr; 02.30.Hq; 02.70.Wz;
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摘要：
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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