Asymptotics and total integrals of the \(\mathrm{P}_{\mathrm{I}}^2\) tritronquée solution and its Hamiltonian

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Asymptotics and summation methods for ordinary differential equations in the complex domain (34M30) Painlevé-type functions (33E17) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Cites Work

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Geometry of the string equations
Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach
On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour
On tronquée solutions of the first Painlevé hierarchy
Weakly nonlinear solutions of equation \(P^ 2_ 1\)
Level-spacing distributions and the Airy kernel
On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo-Miwa-Ueno differential
Large deformations of the Tracy-Widom distribution. I: Non-oscillatory asymptotics
A certain expression of the first Painlevé hierarchy
Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation
On critical behaviour in generalized Kadomtsev-Petviashvili equations
On integrals of the tronquée solutions and the associated Hamiltonians for the Painlevé II equation
``Quantizations of higher Hamiltonian analogues of the Painlevé I and Painlevé II equations with two degrees of freedom
On critical behaviour in systems of Hamiltonian partial differential equations
On the tritronquée solutions of \(\mathrm{P}_{\mathrm{I}}^2\)
Critical behavior for scalar nonlinear waves
Universality of a double scaling limit near singular edge points in random matrix models
Asymptotics of the Gurevich-Pitaevskii universal special solution of the Korteweg-de Vries equation as \(|x|\to\infty\)
Asymptotics for a special solution to the second member of the Painlevé I hierarchy
Universality
The KdV Hierarchy: Universality and a Painlevé Transcendent
Total integrals of global solutions to Painlevé II
Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I
Universality Near the Gradient Catastrophe Point in the Semiclassical <scp>Sine‐Gordon</scp> Equation
Total integrals of Ablowitz‐Segur solutions for the inhomogeneous Painlevé II equation
The existence of a real pole-free solution of the fourth order analogue of the Painlevé I equation
Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.

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