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From Discrete to Continuous Painlevé Equations: A Bilinear Approach

Y. Ohta·A. Ramani·B. Grammaticos·K. M. Tamizhmani
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Abstract

We present the bilinear forms of the (continuous) Painlevé equations obtained from the continuous limit of the analogous expresssions for the discrete ones. The advantage of this method is that it leads to very symmetrical results. A new and interesting result is the bilinearization of the P$_{\rm VI}$ equation, something that was missing till now.

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Y. Ohta, A. Ramani, B. Grammaticos, K. M. Tamizhmani. 1996-03-08. From Discrete to Continuous Painlevé Equations: A Bilinear Approach. https://doi.org/10.1016/0375-9601(96)00292-7

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