We identify the Painleve Lax pairs with those corresponding to stationary solutions of non-isospectral flows, both for partial differential equations and differential-difference equations. We discuss symmetry reductions of integrable differential-difference equations and show that, in contrast with the continuous case, where Painleve' equations naturally arise, in the discrete case the so-called ''discrete Painleve equations'' cannot be obtained in this way. Actually, symmetry reductions of integrable differential-difference equations naturally provide ''delay Painleve equations. ''
Levi, D., Ragnisco, O., Rodriguez, M.a. (1992). ON NONISOSPECTRAL FLOWS, PAINLEVE EQUATIONS, AND SYMMETRIES OF DIFFERENTIAL AND DIFFERENCE-EQUATIONS. THEORETICAL AND MATHEMATICAL PHYSICS, 93(3), 1409-1414 [10.1007/BF01016397].
ON NONISOSPECTRAL FLOWS, PAINLEVE EQUATIONS, AND SYMMETRIES OF DIFFERENTIAL AND DIFFERENCE-EQUATIONS
LEVI, Decio;RAGNISCO, Orlando;
1992-01-01
Abstract
We identify the Painleve Lax pairs with those corresponding to stationary solutions of non-isospectral flows, both for partial differential equations and differential-difference equations. We discuss symmetry reductions of integrable differential-difference equations and show that, in contrast with the continuous case, where Painleve' equations naturally arise, in the discrete case the so-called ''discrete Painleve equations'' cannot be obtained in this way. Actually, symmetry reductions of integrable differential-difference equations naturally provide ''delay Painleve equations. ''I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
