Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin

Abstract

We prove that there exists the unique odd meromorphic solution of dP3, $u(\tau )$ such that $u(0)=0$, and study some of its properties, mainly: the coefficients of its Taylor expansion at the origin and asymptotic behaviour as $\tau \to +\infty$.

Final (journal) version of the paper

References in corpus (2)

• Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painleve' Equation: II
• Asymptotics of Integrals of Some Functions Related to the Degenerate Third Painlevé Equation

Cited by in corpus (2)

• Extreme Superposition: Rogue Waves of Infinite Order and the Painlevé-III Hierarchy
• Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type