Related papers: On the Linearization of the First and Second Painl…
The $(2k)$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k)$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k=1$. The Gauss-Bonnet curvatures are used in theoretical…
The goal of this article is to prove that the determinantal formulas of the Painlev'e 2 system identify with the correlation functions computed from the topological recursion on their spectral curve for an arbitrary non-zero monodromy…
In the present paper authors introduce the L_n-integral transform and the inverse integral transform for n = 2^k, k=0,1,2,..., as a generalization of the classical Laplace transform and the inverse Laplace transform, respectively.…
In this letter we show that the overlap formulation of chiral gauge theories correctly reproduces the gravitational Lorentz anomaly in 2-dimensions. This formulation has been recently suggested as a solution to the fermion doubling problem…
Our aim is to find a general approach to the theory of classical solutions of the Garnier system in $n$-variables, ${\cal G}_n$, based on the Riemann-Hilbert problem and on the geometry of the space of isomonodromy deformations. Our…
We present new second-kind integral-equation formulations of the interior and exterior Dirichlet problems for Laplace's equation. The operators in these formulations are both continuous and coercive on general Lipschitz domains in…
It is investigated how two (standard or generalized) $\lambda-$symmetries of a given second-order ordinary differential equation can be used to solve the equation by quadratures. The method is based on the construction of two commuting…
Link between the Painleve property and the first integrals of nonlinear ordinary differential equations in polynomial form is discussed. The form of the first integrals of the nonlinear differential equations is shown to determine by the…
In the work we use integral formulas for calculating the monodromy data for the Painlev\'e-2 equation. The perturbation theory for the auxiliary linear system is constructed and formulas for the variation of the monodromy data are obtained.…
In this paper, we classify all (complete) non elementary algebraic solutions of Garnier systems that can be constructed by Kitaev's method: they are deduced from isomonodromic deformations defined by pulling back a given fuchsian equation E…
The linearisation of a second-order formulation of the conformal Einstein field equations (CEFEs) in Generalised Harmonic Gauge (GHG), with trace-free matter is derived. The linearised equations are obtained for a general background and…
Under the Flaschka-Newell Lax pair, the Darboux transformation for the Painlev\'{e}-II equation is constructed by the limiting technique. With the aid of the Darboux transformation, the rational solutions are represented by the Gram…
The singular manifold method from the Painleve analysis can be used to investigate many important integrable properties for the nonlinear partial differential equations.In this paper, the two-singular-manifold method is applied to the…
We have shown that two of the most studied models of lineal gravities - Liouville gravity and a ``string-inspired'' model exhibiting the main characteristic features of a black-hole solution - can be formulated as gauge invariant theories…
We will describe natural `Lax pairs' for the difference Painleve equations with affine Weyl symmetry groups of types E6, E7 and E8, showing that they do indeed arise as symmetries of certain Fuchsian systems of differential equations.
Model theoretic ranks of solutions to Painleve equations are calculated, and the type of the generic solution of the second Painleve equation is shown to be disintegrated, strengthening a theorem of Nagloo. A question of Hrushovski and…
We present a linear system of difference equations whose entries are expressed in terms of theta functions. This linear system is singular at $4m+12$ points for $m \geq 1$, which appear in pairs due to a symmetry condition. We parameterize…
In this paper we \emph{explicitly} compute the transformation that maps the generic second order differential equation $y''= f(x, y, y')$ to the Painlev\'e first equation $y''=6y^2+x$ (resp. the Painlev\'e second equation ${y''=2 y^{3}+yx+…
In the first part of this paper we linearize and solve the Van der Pol and Lienard equations with some additional nonlinear terms by the application of a generalized form of Cole-Hopf transformation. We then show that the same…
In this paper, two methods are employed to investigate for which values of the parameters, if any, the two-dimensional real Landau-Ginzburg equation possesses the Painleve property. For an ordinary differential equation to have the Painleve…