Abstract
We construct special solutions for the discrete Painlevé equations. We start with a review of the corresponding solutions in the case of the continuous Painlevé equations and then proceed to construct the solutions in the discrete case. We show how, starting from an elementary, seed solution, one can use the auto-Bäcklund transformations in order to build iteratively ‘higher’ solutions. Using the bilinear formalism we show that the τ-functions for these ‘higher’ solutions can be cast into the form of Casorati determinants.
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Tamizhmani, K., Tamizhmani, T., Grammaticos, B., Ramani, A. Special Solutions for Discrete Painlevé Equations. In: Grammaticos, B., Tamizhmani, T., Kosmann-Schwarzbach, Y. (eds) Discrete Integrable Systems. Lecture Notes in Physics, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40357-9_8
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DOI: https://doi.org/10.1007/978-3-540-40357-9_8
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