4 papers · 1 filter
The WKB Riemann-Hilbert Problem for the Painlevé I System
Mohamad Alameddine, Olivier Marchal, Nikita Nikolaev +1
In this paper, we solve the direct monodromy problem for the Borel-summed -parameter solution of Painlevé~I. Using the auxiliary time equation, we first construct formal WKB wav…
Explicit Hamiltonian structure of the Flaschka-Newell Painlevé II hierarchy via symmetry reduction of the Painlevé IV hierarchy
Olivier Marchal, Mohamad Alameddine, Sergej Laub
We study the Hamiltonian structure of the Flaschka-Newell Painlevé II hierarchy via symmetry reduction of the associated space of meromorphic connections. Building on the realizati…
Universal Correlators on Exponentially Ramified Spectral Curves
Mohamad Alameddine, Alexander Hock
We investigate generalized topological recursion on compact spectral curves admitting exponential, and more generally essential, singularities as ramification points. Exploiting th…
A symmetry reduction of the Painlevé IV hierarchy to the Flaschka-Newell Painlevé II hierarchy
Mohamad Alameddine, Olivier Marchal
We study the isomonodromic deformation problem associated with rank-two meromorphic connections on the Riemann sphere having one regular singularity and one irregular singularity o…