Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painleve' Equation: II

Abstract

The degenerate third Painleve' equation, $u"(t)=(u^{\prime }(t){)}^2/u(t)-u^{\prime }(t)/t+1/t(-8c{u}^2(t)+2ab)+b^2/u(t)$, where $c=+/-1$, $b>0$, and $a$ is a complex parameter, is studied via the Isomonodromy Deformation Method. Asymptotics of general regular and singular solutions $u(t)$ as $t->+/-\infty$ and $t->+/-i\infty$ are derived and parametrized in terms of the monodromy data of the associated 2X2 linear auxiliary problem introduced in the first part of this work [1]. Using these results, three-real-parameter families of solutions that have infinite sequences of zeroes and poles that are asymptotically located along the real and imaginary axes are distinguished: asymptotics of these zeroes and poles are also obtained.

arXiv comment50 pages

References in corpus (7)

• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• Expectation values of local fields in Bullough-Dodd model and integrable perturbed conformal field theories
• Exact Results for Supersymmetric Sigma Models
• On Exact Solutions to the Cylindrical Poisson-Boltzmann Equation with Applications to Polyelectrolytes
• Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painleve' Equation: II
• Strominger--Yau--Zaslow geometry, Affine Spheres and Painlevé III
• Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlevé Equation. I

Cited by in corpus (10)

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• On the Linearization of the Painleve' III-VI Equations and Reductions of the Three-Wave Resonant System
• Open Problems for Painlevé Equations
• Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin
• Existence and Uniqueness of Tronquée Solutions of the Third and Fourth Painlevé Equations
• Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study
• Elizabethan vortices
• Tronquée Solutions of the Third and Fourth Painlevé Equations
• Asymptotics of Integrals of Some Functions Related to the Degenerate Third Painlevé Equation