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      Bäcklund Transformations for First and Second Painlevé Hierarchies

      Sakka, Ayman H. (SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 2009-03-02)
      We give B¨acklund transformations for first and second Painlev´e hierarchies. These B¨acklund transformations are generalization of known B¨acklund transformations of the first and second Painlev´e equations and they ...
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      Linear problems and hierarchies of Painlevé equations

      Sakka, Ayman H. (IOP Publishing, 2009-01-16)
      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 ...
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      On special solutions of second and fourth Painlevé hierarchies

      Sakka, A. H. (Elsevier BV, 2009-02)
      In this article, we give special solutions of second and fourth Painlev´e hierarchies derived by Gordoa, Joshi, and Pickering. We show that for certain choice of the parameters each n-th member of these hierarchies has ...