Power and Exponential Expansions of Solutions to the Third Painleve’ Equation.

Abstract:

By means of Power Geometry, shortly presented in §1, in the generic case we compute all power expansions of solutions to the third Painleve’ equation at points z = 0 (§2) and z = z_{0} ≠ 0 (§3). Analogously we compute all power expansions of solutions to the modified third Painleve equation at points t = 0, t = ∞ (§4), t = t_{0} ≠ 0 (§5), where t = exp(z). In the point t=0 we have found a new type singularity of the modified third Painleve equation.

Publication language:russian, pages:19

Research direction:

Mathematical problems and theory of numerical methods