Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type
arXiv:2110.09858 · doi:10.1063/5.0075416
Abstract
We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher analogues of the Painlev\' e equations are considered as examples.
arXiv comment13 pages
References in corpus (19)
- On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour
- Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach
- Extreme Superposition: Rogue Waves of Infinite Order and the Painlevé-III Hierarchy
- Universality of a double scaling limit near singular edge points in random matrix models
- Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
- The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation
- The Hamiltonian Structure of the Second Painleve Hierarchy
- Influence of small dispersion on self-focusing in spatially one-dimensional case
- Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation
- Asymptotics for a special solution to the second member of the Painleve I hierarchy
- Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlevé-II equation
- On matrix Painlevé II equations
- Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation
- Nonautonomous symmetries of the KdV equation and step-like solutions
- On an isomonodromy deformation equation without the Painlevé property
- Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin
- Large and infinite order solitons of the coupled nonlinear Schrödinger equation
- Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation
- Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study