D. Levi, O. Ragnisco, M. A. Rodriguez, “On non-isospectral flows, Painlevé equations, and symmetries of differential and difference equations”, TMF, 93:3 (1992), 473–480; Theoret. and Math. Phys., 93:3 (1992), 1409

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 93, Number 3, Pages 473–480 (Mi tmf1539)

This article is cited in 41 scientific papers (total in 41 papers)

On non-isospectral flows, Painlevé equations, and symmetries of differential and difference equations

D. Levi^a, O. Ragnisco^b, M. A. Rodriguez^b

^a INFN — National Institute of Nuclear Physics
^b Universidad Complutense, Departamento de Fisica Teorica II

Full-text PDF (629 kB) Citations (41)

References:

PDF

HTML

Abstract: We identify the Painlevé Lax pairs with those corresponding to stationary solutions of non-isospectral flows, both for partial differential equations and differential-difference equations. We discuss symmetry reductions of integrable differential-difference equations and show that, in contrast with the continuous case, where Painlevé equations naturally arise, in the discrete case the so-called “discrete Painlevé equations” cannot be obtained in this way. Actually, symmetry reductions of integrable differential-difference equations naturally provide “delay Painlevé equations”.

Received: 18.06.1992

English version:
Theoretical and Mathematical Physics, 1992, Volume 93, Issue 3, Pages 1409–1414
DOI: https://doi.org/10.1007/BF01016397

Bibliographic databases:

Language: English

Citation: D. Levi, O. Ragnisco, M. A. Rodriguez, “On non-isospectral flows, Painlevé equations, and symmetries of differential and difference equations”, TMF, 93:3 (1992), 473–480; Theoret. and Math. Phys., 93:3 (1992), 1409–1414

Citation in format AMSBIB

\Bibitem{LevRagRod92}

\by D.~Levi, O.~Ragnisco, M.~A.~Rodriguez

\paper On non-isospectral flows, Painlev\'e equations, and symmetries of differential and difference equations

\jour TMF

\yr 1992

\vol 93

\issue 3

\pages 473--480

\mathnet{http://mi.mathnet.ru/tmf1539}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1233554}

\zmath{https://zbmath.org/?q=an:0801.35122}

\transl

\jour Theoret. and Math. Phys.

\yr 1992

\vol 93

\issue 3

\pages 1409--1414

\crossref{https://doi.org/10.1007/BF01016397}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992LK67300006}

Linking options:

https://www.mathnet.ru/eng/tmf1539

https://www.mathnet.ru/eng/tmf/v93/i3/p473

This publication is cited in the following 41 articles:

P.R. Gordoa, A. Pickering, “The extended second Painlevé hierarchy: Auto-Bäcklund transformations and special integrals”, Journal of Differential Equations, 417 (2025), 132
Pilar Ruiz Gordoa, Andrew Pickering, “Auto‐Bäcklund Transformations for New Matrix First and Second Painlevé Hierarchies”, Stud Appl Math, 154:1 (2025)
P. Gordoa, A. Pickering, Contemporary Mathematics, 807, Recent Progress in Special Functions, 2024, 131
Xiang-Ke Chang, Xiao-Min Chen, “On the peakon dynamical system of the second flow in the Camassa–Holm hierarchy”, Advances in Mathematics, 459 (2024), 110000
P.R. Gordoa, A. Pickering, J.A.D. Wattis, “Solution classes of the matrix second Painlevé hierarchy”, Physica D: Nonlinear Phenomena, 435 (2022), 133295
P.R. Gordoa, A. Pickering, “On matrix fourth Painlevé hierarchies”, Journal of Differential Equations, 271 (2021), 499
Alain Moise Dikandé, Eugene Chenui Aban, Anderson Sunda‐Meya, “Thermal lensing‐induced soliton molecules in β‐phase gallium oxide”, Micro & Optical Tech Letters, 63:12 (2021), 3100
Levi D. Rodriguez M.A. Thomova Z., “The Discretized Boussinesq Equation and Its Conditional Symmetry Reduction”, J. Phys. A-Math. Theor., 53:4 (2020), 045201
Gordoa P.R. Pickering A., “Backlund Transformations For a New Extended Painleve Hierarchy”, Commun. Nonlinear Sci. Numer. Simul., 69 (2019), 78–97
Andrew Pickering, Pilar R. Gordoa, Jonathan A.D. Wattis, “The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: Scalar and matrix cases”, Physica D: Nonlinear Phenomena, 391 (2019), 72
Yu Liu, Huanhe Dong, Yong Zhang, “Solutions of a discrete integrable hierarchy by straightening out of its continuous and discrete constrained flows”, Anal.Math.Phys., 9:1 (2019), 465
P.R. Gordoa, A. Pickering, “Auto-Bäcklund transformations for a matrix partial differential equation”, Physics Letters A, 382:29 (2018), 1908
Gordoa P.R., Pickering A., “On An Extended Second Painlevé Hierarchy”, J. Differ. Equ., 263:7 (2017), 4070–4125
Yufeng Zhang, Xiangzhi Zhang, “Two kinds of discrete integrable hierarchies of evolution equations and some algebraic-geometric solutions”, Adv Differ Equ, 2017:1 (2017)
Gordoa P.R., Pickering A., Zhu Z.N., “On matrix Painlevé hierarchies”, J. Differ. Equ., 261:2 (2016), 1128–1175
Hietarinta J. Joshi N. Nijhoff F., “Discrete Systems and Integrability”, Discrete Systems and Integrability, Cambridge Texts in Applied Mathematics, Cambridge Univ Press, 2016, 1–445
Yu-Feng Zhang, Yan Wang, “Generating integrable lattice hierarchies by some matrix and operator Lie algebras”, Adv Differ Equ, 2016:1 (2016)
Gordoa P.R. Pickering A. Wattis J.A.D., “Nonisospectral Scattering Problems and Similarity Reductions”, Appl. Math. Comput., 237 (2014), 77–84
Gordoa P.R., Pickering A., Senthilvelan M., “The Prelle-Singer Method and Painlevé Hierarchies”, J. Math. Phys., 55:5 (2014), 053510
Adam Doliwa, “Non-commutativeq-Painlevé VI equation”, J. Phys. A: Math. Theor., 47:3 (2014), 035203

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	382
Full-text PDF :	143
References:	58
First page:	1

Что такое QR-код?

Registration to the website

Logotypes