Quantum curves and q-deformed Painlevé equations
Sign Up to like & getrecommendations! Published in 2019 at "Letters in Mathematical Physics"
DOI: 10.1007/s11005-019-01174-y
Abstract: We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus one mirror curve, these are conjectured to be the q-difference Painlevé equations… read more here.
Keywords: quantum curves; painlev equations; tau functions; topological string ... See more keywords
Doubly-Resonant Saddle-Nodes in $$\mathbb {C}^{3}$$C3 and the Fixed Singularity at Infinity in the Painlevé Equations: Formal Classification
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DOI: 10.1007/s12346-016-0214-z
Abstract: In this work we consider formal singular vector fields in $$\mathbb {C}^{3}$$C3 with an isolated and doubly-resonant singularity of saddle-node type at the origin. Such vector fields come from irregular two-dimensional systems with two opposite… read more here.
Keywords: painlev equations; singularity infinity; doubly resonant; singularity ... See more keywords
Hierarchies of q-discrete Painlevé equations
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Nonlinear Mathematical Physics"
DOI: 10.1080/14029251.2020.1757235
Abstract: In this paper, we construct a new hierarchy based on the third q-discrete Painlevé equation (qPIII) and also study the hierarchy of the second q-discrete Painlevé equation (qPII). Both hierarchies are derived by using reductions… read more here.
Keywords: equation; discrete painlev; painlev equations; hierarchies discrete ... See more keywords