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"Quantization" of higher hamiltonian analogues of the Painleve I and Painleve II equations with two degrees of freedom
Quantization higher hamiltonian analogues Painleve I Painleve II equations Exactly Solvable and Integrable Systems
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2012/4/27
We construct a solution of an analog of the Schr\"{o}dinger equation for the Hamiltonian $ H_I (z, t, q_1, q_2, p_1, p_2) $ corresponding to the second equation $P_1^2$ in the Painleve I hierarchy. Th...
Pade interpolation for elliptic Painleve equation
Pade interpolation elliptic Painleve equation Mathematical Physics
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2012/4/17
An interpolation problem related to the elliptic Painlev\'e equation is formulated and solved. A simple form of the elliptic Painlev\'e equation and the Lax pair are obtained. Explicit determinant for...
Quantum Painleve-Calogero Correspondence
Quantum Painleve-Calogero Correspondence Mathematical Physics
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2011/9/22
Abstract: The Painleve-Calogero correspondence is extended to auxiliary linear problems associated with Painleve equations. The linear problems are represented in a new form which has a suggestive int...