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Point classification of the second order ODE's by Ruslan Sharipov and its application to Painleve equations
Point classification the second order ODE's Ruslan Sharipov Painleve equations
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2012/4/17
This is an review on the point classification of second order ODE's by Ruslan Sharipov. His works were published in 1997-1998 at the Electronic Archive at LANL and undeservedly forgotten. Last chapter...
A note on the R. Fuchs's problem for the Painleve equations
Painleve equations Isomonodromic deformation Ordinary differential equations
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2012/4/17
In this article we consider a first-order completely integrable system of partial differential equations $\partial \Fi/partial x=A(x, t) \Fi, \partial \Fi/partial t=B(x, t) \Fi$ with $\Fi=(\fi_1, \fi_...
Integrable Origins of Higher Order Painleve Equations
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
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2010/11/10
Higher order Painleve equations invariant under extended affine Weyl groups $A^{(1)}_n$ are obtained through self-similarity limit of a class of pseudo-differential Lax hierarchies with symmetry inher...
The lattice structure of connection preserving deformations for q-Painleve equations I
Exactly Solvable and Integrable Systems (nlin.SI)
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2010/11/10
We wish to explore a link between the Lax integrability of the q-Painleve equations and the symmetries of the q-Painleve equations. To do this, we consider the set of associated linear problems for th...