Multi-component Painlev\'e ODE's and related non-autonomous KdV stationary hierarchies
Abstract
First, starting from two hierarchies of autonomous St\"ackel ODE's, we reconstruct the hierarchy of KdV stationary systems. Next, we deform considered autonomous St\"ackel systems to non-autonomous Painlev\'e hierarchies of ODE's. Finally, we reconstruct the related non-autonomous KdV stationary hierarchies from respective Painlev\'e systems.
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