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Soliton structures for the (3 + 1)-dimensional Painlevé integrable equation in fluid mediums [PDF]
Scientific ReportsThe (3 + 1)-dimensional Painlevé integrable equation are a class of nonlinear differential equations with special properties, which play an important role in nonlinear science and are of great significance in solving various practical problems, such as ...
Jian-Guo Liu
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AGT correspondence, (q-)Painlevè equations and matrix models
Nuclear Physics B, 2022 Painlevè equation for conformal blocks is a combined corollary of integrability and Ward identities, which can be explicitly revealed in the matrix model realization of AGT relations.
A. Mironov +3 more
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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
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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
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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
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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
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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
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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
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Mathematics, 2022 The family of the generalized Schrödinger equations with Kerr nonlinearity of unrestricted order is considered. The solutions of equations are looked for using traveling wave reductions. The Painlevé test is applied for finding arbitrary constants in the
Nikolay A. Kudryashov
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Journal of Ocean Engineering and Science, 2023 This article considers time-dependent variable coefficients (2+1) and (3+1)-dimensional extended Sakovich equation. Painlevé analysis and auto-Bäcklund transformation methods are used to examine both the considered equations.
Shailendra Singh, S. Saha Ray
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