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|Title||Linear problems and hierarchies of Painlevé equations|
|Title in Arabic||Linear problems and hierarchies of Painlevé equations|
In this paper, we show that the expansion of linear problems of the Painlev´e equation in powers of the spectral variable can be used to derive hierarchies of ordinary differential equations. We applied this approach to linear problems of the first, second, third and fourth Painlev´e equations. We derived a new hierarchy of the third Painlev´e equation and rederived known hierarchies of the other equations. Moreover some special solutions of the hierarchies of the second, third and fourth Painlev´e equations are also given.
|Published in||Journal of Physics A: Mathematical and Theoretical|
|Series||Vol. 42, No. 2|
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