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.
Kecker:Space of initial conditions for a cubic Hamiltonian system
3 Pith papers cite this work. Polarity classification is still indexing.
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Linear collisional kinetic equations without confinement exhibit long-time self-similar behavior, with rescaled solutions converging uniformly to diffusion limits via Wild sums.
A discrete-time constant flux condition on the heat equation forces the domain to be a ball under suitable regularity.
citing papers explorer
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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.
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Self-similarity and diffusive limits for linear kinetic equations: a Wild sum approach
Linear collisional kinetic equations without confinement exhibit long-time self-similar behavior, with rescaled solutions converging uniformly to diffusion limits via Wild sums.
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A discrete-time overdetermined problem for the heat equation
A discrete-time constant flux condition on the heat equation forces the domain to be a ball under suitable regularity.