15 research outputs found
Backlund transformations for discrete Painleve equations: Discrete P-II-P-V
Cataloged from PDF version of article.Transformation properties of discrete Painleve´ equations are investigated by using an algorithmic method. This
method yields explicit transformations which relates the solutions of discrete Painleve´ equations, discrete PII–PV, with
different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the
classical special functions of discrete Painleve´ equations can also be obtained from these transformations.
2005 Elsevier Ltd. All rights reserved
Schlessinger Transformations for Painleve VI equation
Cataloged from PDF version of article.A method to obtain the Schlesinger transformations for Painlevi VI equation is
given. The procedure involves formulating a Riemann-Hilbert problem for a transformation
matrix which transforms the solution of the linear problem but leaves the
associated monodromy data the same. 0 1995 American Institute of Physics
Second-order second-degree Painleve equations related with Painleve I-IV equations and Fuchsian-type transformations
Cataloged from PDF version of article.One-to-one correspondence between the Painlevé I-VI equations and certain second-order second-degree equations of Painlevé type is investigated. The transformation between the Painlevé equations and second-order second-degree equations is the one involving the Fuchsian-type equation. © 1999 American Institute of Physics
Third order differential equations with fixed critical points
Cataloged from PDF version of article.The singular point analysis of third order ordinary differential equations which are algebraic in y and y′ is presented. Some new third order ordinary differential equations that pass the Painlevé test as well as the known ones are found. © 2008 Elsevier Inc. All rights reserved
On the solvability of the discrete second Painlevé equation
The inverse monodromy method for studying the Riemann-Hilbert problem associated with classical Painlevé equations is applied to the discrete second Painlevé equation
A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators
We explore a nonlocal connection between certain linear and nonlinear
ordinary differential equations (ODEs), representing physically important
oscillator systems, and identify a class of integrable nonlinear ODEs of any
order. We also devise a method to derive explicit general solutions of the
nonlinear ODEs. Interestingly, many well known integrable models can be
accommodated into our scheme and our procedure thereby provides further
understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres
Square lattice Ising model susceptibility: Series expansion method and differential equation for
In a previous paper (J. Phys. A {\bf 37} (2004) 9651-9668) we have given the
Fuchsian linear differential equation satisfied by , the
``three-particle'' contribution to the susceptibility of the isotropic square
lattice Ising model. This paper gives the details of the calculations (with
some useful tricks and tools) allowing one to obtain long series in polynomial
time. The method is based on series expansion in the variables that appear in
the -dimensional integrals representing the -particle contribution to
the isotropic square lattice Ising model susceptibility . The
integration rules are straightforward due to remarkable formulas we derived for
these variables. We obtain without any numerical approximation as
a fully integrated series in the variable , where , with the conventional Ising model coupling constant. We also
give some perspectives and comments on these results.Comment: 28 pages, no figur
A Lagrangian Description of the Higher-Order Painlev\'e Equations
We derive the Lagrangians of the higher-order Painlev\'e equations using
Jacobi's last multiplier technique. Some of these higher-order differential
equations display certain remarkable properties like passing the Painlev\'e
test and satisfy the conditions stated by Jur\'a, (Acta Appl. Math.
66 (2001) 25--39), thus allowing for a Lagrangian description.Comment: 16 pages, to be published in Applied Mathematics and Computatio
On the solvability of the discrete second Painleve equation
Cataloged from PDF version of article.The inverse monodromy method for studying the Riemann-Hilbert problem associated with classical Painlevé equations is applied to the discrete second Painlevé equation. © 2011 IOP Publishing Ltd
On the solvability of the Painleve VI equation
A rigorous method was introduced by Fokas and Zhou (1992) for studying the Riemann-Hilbert problem associated with the Painleve II and IV equations. The same methodology has been applied to the Painleve I, III and V equations. In this paper, we will apply the same methodology to the Painleve VI equation. We will show that the Cauchy problem for the Painleve VI equation admits, in general, a global meromorphic solution in t. Furthermore, the special solution which can be written in terms of a hypergeometric function is obtained via solving the special case of the Riemann-Hilbert problem