Second-order second degree Painlevé equations related with Painlevé I, II, III equations
نویسندگان
چکیده
The algorithmic method introduced by Fokas and Ablowitz to investigate the transformation properties of Painlevé equations is used to obtain a one-to-one correspondence between the Painlevé I, II and III equations and certain second-order second degree equations of Painlevé type.
منابع مشابه
On WKB analysis of higher order Painlevé equations with a large parameter
We announce a generalization of the reduction theorem for 0parameter solutions of the traditional (i.e., second order) Painlevé equations with a large parameter to those of some higher order Painlevé equations, i.e., each member of the Painleve hierarchies (PJ) (J =I, II-1 and II-2) discussed in [KKNT]. Thus the scope of applicability of the reduction theorem ([KT1], [KT2]) has been substantial...
متن کاملOn Some Hamiltonian Structures of Painlevé Systems, I
In this series of papers, we study some Hamiltonian structures of Painlevé systems (HJ ), J = V I, V, IV, III, II, I, namely, symplectic structures of the spaces for Painlevé systems constructed by K. Okamoto([7]), and a characterization of Painlevé systems by their spaces. As is well known, P. Painlevé and B. Gambier discovered, at the beginning of this century, six nonlinear second order diff...
متن کاملOn the discrete and continuous Miura Chain associated with the Sixth Painlevé Equation
A Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or Bäcklund transformations. We describe such a chain for the sixth Painlevé equation (PVI), containing, apart from PVI itself, a Schwarzian version as well as a second-order second-degree ordinary differential equation (ODE). As a byproduct we derive an auto-Bäcklund transformation, relatin...
متن کاملPainlevé Test and Higher Order Differential Equations
Starting from the second Painlevé equation, we obtain Painlevé type equations of higher order by using the singular point analysis.
متن کاملOn the algebraic solutions of the sixth Painlevé equation related to second order Picard-Fuchs equations
We describe two algebraic solutions of the sixth Painlevé equation which are related to (isomonodromic) deformations of Picard-Fuchs equations of order two. 1 Statement of the result In this note we describe two algebraic solutions of the following Painlevé VI ( PV I) equation dλ dt2 = 1 2 ( 1 λ + 1 λ− 1 + 1 λ− t )( dλ dt ) − ( 1 t + 1 t− 1 + 1 λ− t ) dλ dt + λ(λ− 1)(λ− t) t2(t2 − 1) [α + β t λ...
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 1997