Painleve Chains for the Study of Integrable Higher Order Differential Equations.
GEORGIA UNIV ATHENS DEPT OF CHEMISTRY
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A previous paper defines the three fundamental homogeneous active Painleve chains which are generated from the equation u sub 2x ku sub 2, u sub 2x ku sub 3, and ux ku sub 2. This paper shows how the concept of Painleve chains can be extended to Painleve chains generated from hybrid differential equations and the passive differential equation u sub 2 ku 2 over x. In addition the Schwarzian derivative can be used to generate a Painleve chain with the interesting property of consecutive integral resonances. Finally the 2 x 2 eigenvalue problem of Zakharov and Shabat is shown to generate chains exhibiting some but not all of the features of Painleve chains.
- Numerical Mathematics