Second-order second degree Painlevé equations related with Painlevé I, II, III equations
Journal of Physics A: Mathematical and General
Institute of Physics Publishing Ltd.
5159 - 5177
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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.