Matrix Painlevé II equations
نویسندگان
چکیده
The Painlev\'e--Kovalevskaya test is applied to find three matrix versions of the Painlev\'e II equation. All these equations are interpreted as group-invariant reductions integrable evolution equations, which makes it possible construct isomonodromic Lax pairs for them.
منابع مشابه
Discrete Painlevé Equations and Random Matrix Averages
The τ-function theory of Painlevé systems is used to derive recurrences in the rank n of certain random matrix averages over U (n). These recurrences involve auxilary quantities which satisfy discrete Painlevé equations. The random matrix averages include cases which can be interpreted as eigenvalue distributions at the hard edge and in the bulk of matrix ensembles with unitary symmetry. The re...
متن کاملGalois Theory and Painlevé Equations
— The paper consists of two parts. In the first part, we explain an excellent idea, due to mathematicians of the 19-th century, of naturally developing classical Galois theory of algebraic equations to an infinite dimensional Galois theory of nonlinear differential equations. We show with an instructive example how we can realize the idea of the 19-th century in a rigorous framework. In the sec...
متن کاملStudies on the Painlevé equations V , third Painlevé
By means of geometrical classification ([22]) of space of initial conditions, it is natural to consider the three types, PIII(D6), PIII(D7) and PIII(D8), for the third Painlevé equation. The fourth article of the series of papers [17] on the Painlevé equations is concerned with PIII(D6), generic type of the equation. The other two types, PIII(D7) and PIII(D8) are obtained as degeneration from P...
متن کاملNew Expressions for Discrete Painlevé Equations
Discrete Painlevé equations are studied from various points of view as integrable systems [2], [7]. They are discrete equations which are reduced to the Painlevé differential equations in a suitable limiting process, and moreover, which pass the singularity confinement test. Passing this test can be thought of as a difference version of the Painlevé property. The Painlevé differential equations...
متن کاملA numerical methodology for the Painlevé equations
The six Painlevé transcendents PI -PV I have both applications and analytic properties that make them stand out from most other classes of special functions. Although they have been the subject of extensive theoretical investigations for about a century, they still have a reputation for being numerically challenging. In particular, their extensive pole fields in the complex plane have often bee...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical and Mathematical Physics
سال: 2021
ISSN: ['1864-5887', '1864-5879']
DOI: https://doi.org/10.1134/s0040577921050020