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The algorithmic method introduced by Fokas and Ablowitz to investigate the transformation properties of Painlevé equations is used to obtain a one-to-one correspondence between the Painlevé I, II and III equations and certain second-order second degree equations of Painlevé type.

- Ugurhan Mugan
- 2004

The singular point analysis of third-order ordinary differential equations in the nonpolynomial class are presented. Some new third order ordinary differential equations which pass the Painlevé test as well as the known ones are found.

- Ugurhan Mugan
- 2001

Starting from the second Painlevé equation, we obtain Painlevé type equations of higher order by using the singular point analysis.

- Fahd Jrad, Ugurhan Mugan
- 2005

Painlevé and his school [1 – 3] studied the certain class of second order ordinary differential equations (ODEs) and found fifty canonical equations whose solutions have no movable critical points. This property is known as the Painlevé property. Distinguished among these fifty equations are six Painlevé equations, PI – PVI. The six Painlevé transcendents… (More)

- Ugurhan Mugan
- 2003

Starting from the first Painlevé equation, Painlevé type equations of higher order are obtained by using the singular point analysis.

Transformation properties of discrete Painlevé equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painlevé equations, dPIIdPV, with different parameters. Rational solutions and elementary solutions of discrete Painlevé equations can also be obtained from these… (More)

- Ayman Sakka, Ugurhan Mugan
- 2008

The first-order second-degree equations satisfying the Fuchs theorem concerning the absence of movable critical points, related with Painlevé equations, and one-parameter families of solutions which solve the first-order second-degree equations are investigated.

- Yasin Adjabi, Fahd Jrad, Arezki Kessi, Ugurhan Mugan
- Applied Mathematics and Computation
- 2009

The singular point analysis of third order ordinary differential equations which are algebraic in y and y′ is presented. Some new third order ordinary differential equations that pass the Painlevé test as well as the known ones are found. Corresponding author. E-mail: mugan@fen.bilkent.edu.tr

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