Connection formulae for asymptotics of solutions of the degenerate third Painleve equation: II

The degenerate third Painleve equation, u ''(tau) = (u'(tau))(2)/u(tau) - u'(tau)/tau + 1/tau(-8 epsilon u(2)(tau) + 2ab) + b(2)/u(tau), where epsilon = +/- 1, b is an element of R\{0} and a is an element of C, is studied via the isomonodromy deformation method. Asymptotics of general regular and singular solutions as tau -> +/-infinity and tau -> +/- i infinity are derived and parametrized in terms of the monodromy data of the associated 2 x 2 linear auxiliary problem introduced in Kitaev and Vartanian (2004 Inverse Problems 20 1165-206). Using these results, three real-parameter families of solutions that have infinite sequences of zeros and poles that are asymptotically located along the real and imaginary axes are distinguished: asymptotics of these zeros and poles are also obtained.