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# Finite-order meromorphic solutions and the discrete painleve equations

preprint

posted on 2005-08-16, 13:13 authored by R.G. Halburd, R.J. KorhonenLet w(z) be a finite-order meromorphic solution of the second-order difference equation
w(z+1)+w(z-1) = R(z,w(z)) (1)
where R(z,w(z)) is rational in w(z) and meromorphic in z. Then either w(z) satisfies a difference linear or Riccati equation or else equation (1) can be transformed to one of a list of canonical difference equations. This list consists of all known difference Painleve equation of the form (1), together with their autonomous versions. This suggests that the existence of finite-order meromorphic solutions is a good detector of integrable difference equations.

## History

## School

- Science

## Department

- Mathematical Sciences

## Pages

377236 bytes## Publication date

2005## Notes

This is a pre-print.## Language

- en