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. ''
1992
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/120704
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