On some Hamiltonian structures of coupled Painlevé II systems in dimension four

2007/04/22 by Yusuke Sasano, Sasano, Yusuke
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math-ph #math.AG #math.CA #math.DS #math.MP #msc:14E05 #msc:14E15 #msc:20F55 #msc:34M55

paper · pdf · doi:10.48550/arxiv.0704.2863

9 pages

arxiv created 2011/01/06 · arxiv updated 2011/01/07

Abstract

We find and study a two-parameter family of coupled Painlevé II systems in dimension four with affine Weyl group symmetry of several types. Moreover, we find a three-parameter family of polynomial Hamiltonian systems in two variables t,s. Setting s=0, we can obtain an autonomous version of the coupled Painlevé II systems. We also show its symmetry and holomorphy conditions.

Citations

• Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes

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