The Painlevé transcendents with solvable monodromy
نویسنده
چکیده
We will study special solutions of the fourth, fifth and sixth Painlevé equations with generic values of parameters whose linear monodromy can be calculated explicitly. We will show the relation between Umemura’s classical solutions and our solutions.
منابع مشابه
On Stieltjes relations, Painlevé-IV hierarchy and complex monodromy
A generalisation of the Stieltjes relations for the Painlevé-IV transcendents and their higher analogues determined by the dressing chains is proposed. It is proven that if a rational function from a certain class satisfies these relations it must be a solution of some higher Painlevé-IV equation. The approach is based on the interpretation of the Stieltjes relations as local trivial monodromy ...
متن کاملShear-Free Relativistic Fluids and the Absence of Movable Branch Points
The problem of determining the metric for a non-static shear-free spherically symmetric fluid (either charged or neutral) reduces to the problem of determining a one parameter family of solutions to a second-order ODE containing two arbitrary functions f and g. Choices for f and g are determined such that this ODE admits a one-parameter family of solutions that have poles as their only movable ...
متن کاملOn the asymptotics of the real solutions to the general sixth Painlevé equation
The mathematical and physical significance of the six Painlevé transcendents has been well established. In the last 20 to 30 years, many mathematicians have spent dramatic effort on studying the properties of these transcendents. Although it is the most complicated one among the six Painlevé equations, there have been many results about the sixth Painlevé transcendent. In fact, the asymptotics ...
متن کاملMonodromy of Certain Painleve’–vi Transcendents and Reflection Groups
We study the global analytic properties of the solutions of a particular family of Painlevé VI equations with the parameters β = γ = 0, δ = 2 and 2α = (2μ−1)2 with arbitrary μ, 2μ 6∈ Z. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in th...
متن کاملApplication of uniform asymptotics method to analyzing the asymptotic behaviour of the general fourth Painlevé transcendent
With more and more discovery of their applications in the areas of physics such as quantum mechanics and solitons, Painlevé transcendents have attracted significant attention of many mathematicians in about the last twenty years. One direction of the research in this area is to find the asymptotics behaviour of the Painlevé transcendents as their independent variable approaches the singular poi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007