From Discrete to Continuous Painlevé Equations: A Bilinear Approach

Details From Discrete to Continuous Painlevé Equations: A Bilinear Approach From Discrete to Continuous Painlevé Equations: A Bilinear Approach

1996-03-08

arxiv.org/abs/solv-int/9603002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, plainTeX

Scientific paper

10.1016/0375-9601(96)00292-7

We present the bilinear forms of the (continuous) Painlev\'e 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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