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

الأصل · EN

The degenerate third Painleve' equation, u"(t)=(u'(t))²/u(t)-u'(t)/t+1/t(-8c u²(t)+2ab)+b²/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 -> +/-∞ and t -> +/-i∞ 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.