Results 1 to 10 of about 1,222,314 (174)

On a Dirichlet boundary value problem for an Ermakov–Painlevé I equation. A Hamiltonian EPI system [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2023
Here, a proto-type Ermakov–Painlevé I equation is introduced and a homogeneous Dirichlet-type boundary value problem analysed. In addition, a novel Ermakov–Painlevé I system is set down which is reducible by an involutory transformation to the autonomous
Pablo Amster, Colin Rogers
doaj   +4 more sources

Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation

Advances in Mathematical Physics, 2021
In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear
Irfan Mahmood, Muhammad Waseem
doaj   +2 more sources

On the polynomial solution of the first Painlevé equation

International Journal of Applied Mathematical Research, 2017
The Painlevé equations and their solutions arises in pure, applied mathematics and theoretical physics. In this manuscript we apply the Optimal Homotopy Asymptotic Method (OHAM) for solving the first Painlevé equation. Our approximation technique is based on the use of polynomial solutions, which are shown to be accurate when compared to the computed
D. Sierra Porta, L. A. Núñez
openaire   +2 more sources

On Gevrey orders of formal power series solutions to the third and fifth Painlevé equations near infinity [PDF]

Opuscula Mathematica, 2014
The question under consideration is Gevrey summability of formal power series solutions to the third and fifth Painlevé equations near infinity. We consider the fifth Painlevé equation in two cases: when \(\alpha\beta\gamma\delta \neq 0\) and when ...
Anastasia V. Parusnikova
doaj   +1 more source

On meromorphic solutions of the equations related to the first Painlevé equation

Журнал Белорусского государственного университета: Математика, информатика, 2022
In this paper, we consider the generalised hierarchy of the first Painlevé equation which is a sequence of polynomial ordinary differential equations of even order that have a uniform differential-algebraic structure determined by the operator L~n.
Elena V. Gromak
doaj   +1 more source

Solutions of the third Painlevé equation I [PDF]

Nagoya Mathematical Journal, 1998
Abstract.We classify transcendental classical solutions of the third Painlevé equation. This result combined with the list of algebraic solutions in [11] gives a complete table of classical solutions of the third Painlevé equation.
Umemura, Hiroshi, Watanabe, Humihiko
openaire   +3 more sources

Solutions of the second and fourth Painlevé equations, I [PDF]

Nagoya Mathematical Journal, 1997
AbstractA rigorous proof of the irreducibility of the second and fourth Painlevé equations is given by applying Umemura’s theory on algebraic differential equations ([26], [27], [28]) to the two equations. The proof consists of two parts: to determine a necessary condition for the parameters of the existence of principal ideals invariant under the ...
Umemura, Hiroshi, Watanabe, Humihiko
openaire   +3 more sources

Novel Bäcklund Transformations for Integrable Equations

Mathematics, 2022
In this paper, we construct a new matrix partial differential equation having a structure and properties which mirror those of a matrix fourth Painlevé equation recently derived by the current authors.
Pilar Ruiz Gordoa, Andrew Pickering
doaj   +1 more source

Painlevé Test and Exact Solutions for (1 + 1)-Dimensional Generalized Broer–Kaup Equations

Mathematics, 2022
In this paper, the Painlevé integrable property of the (1 + 1)-dimensional generalized Broer–Kaup (gBK) equations is first proven. Then, the Bäcklund transformations for the gBK equations are derived by using the Painlevé truncation.
Sheng Zhang, Bo Xu
doaj   +1 more source

On Properties of meromorphic solutions of difference Painlevé I and II equation

Global Journal of Mathematical Analysis, 2017
In this paper, we investigate some properties of finite order transcendental meromorphic solutions of difference Painlev \(\)\acute{e}\) I and II equations, and obtain precise estimations of exponents of convergence of poles of difference \(\)\Delta w(z)=w(z+1)-w(z)\) and divided difference \(\)\frac{\Delta w(z)}{w(z)}\), and of fixed points of \(\)w(z+
Weimin Xue, Yanmei Teng
openaire   +2 more sources