Abstract:
We use the inverse monodromy transform to find the fourth Painlevé hierarchy. The second and third members of this hierarchy are given. Special and rational solutions of the second and third members for the $P_4$ hierarchy are discussed. We apply the Painlevé test to the second member of the fourth Painlevé hierarchy.
Keywords:fourth Painlevé hierarchy, fourth Painlevé equation, Painlevé test, special and rational solutions.
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