The authors derive all polynomial Hamiltonians of degrees 3, 4, 5 and 7 with only meromorphic solutions, producing 12 standard forms including new quartic and quintic examples for modified Painlevé equations, with none existing for degree 6 or higher.
Painlevé:Mémoire sur les équations différentielles dont l’intégrale générale est uniforme
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Modified Painlev\'e systems with meromorphic solutions for polynomial Hamiltonians of all degrees
The authors derive all polynomial Hamiltonians of degrees 3, 4, 5 and 7 with only meromorphic solutions, producing 12 standard forms including new quartic and quintic examples for modified Painlevé equations, with none existing for degree 6 or higher.