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Classification of Second Order Painlevé Type Equations Under the Mei Symmetrical Transformations
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Abstract
Ince provided fifty second-order ordinary differential equations of Painlevé type. In this paper, the Mei symmetries correspond to the Lagrangian of the Painlevé-Gambier classification are investigated as well as the Mei invariants along with their respective gauge functions. On the basis of the number of Mei symmetries , these equations are classified. The existence of Mei symmetries can be correlated with the autonomous and non-autonomous properties of ordinary differential equations of Painlevé type.
MSC (2020). 76M60; 22E70; 35A30; 58J70
Title: Classification of Second Order Painlevé Type Equations Under the Mei Symmetrical Transformations
Description:
Abstract
Ince provided fifty second-order ordinary differential equations of Painlevé type.
In this paper, the Mei symmetries correspond to the Lagrangian of the Painlevé-Gambier classification are investigated as well as the Mei invariants along with their respective gauge functions.
On the basis of the number of Mei symmetries , these equations are classified.
The existence of Mei symmetries can be correlated with the autonomous and non-autonomous properties of ordinary differential equations of Painlevé type.
MSC (2020).
76M60; 22E70; 35A30; 58J70.
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