A. B. Shabat, “On the Laplace–Darboux theory of transformations”, TMF, 103:1 (1995), 170–175; Theoret. and Math. Phys., 103:1 (1995), 482

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, 1995, Volume 103, Number 1, Pages 170–175 (Mi tmf1294)

This article is cited in 14 scientific papers (total in 14 papers)

On the Laplace–Darboux theory of transformations

A. B. Shabat

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Full-text PDF (530 kB) Citations (14)

References:

PDF

HTML

Abstract: In the framework of the classical Laplace–Darboux theory the formula of the fractional-rational transformations of the solutions of the linear second order partial differential equation with the two independent variables is established. The one-dimensional reduction discussed briefly.

Received: 28.02.1995

English version:
Theoretical and Mathematical Physics, 1995, Volume 103, Issue 1, Pages 482–485
DOI: https://doi.org/10.1007/BF02069791

Bibliographic databases:

Language: Russian

Citation: A. B. Shabat, “On the Laplace–Darboux theory of transformations”, TMF, 103:1 (1995), 170–175; Theoret. and Math. Phys., 103:1 (1995), 482–485

Citation in format AMSBIB

\Bibitem{Sha95}

\by A.~B.~Shabat

\paper On the Laplace--Darboux theory of transformations

\jour TMF

\yr 1995

\vol 103

\issue 1

\pages 170--175

\mathnet{http://mi.mathnet.ru/tmf1294}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1470941}

\zmath{https://zbmath.org/?q=an:0855.35004}

\transl

\jour Theoret. and Math. Phys.

\yr 1995

\vol 103

\issue 1

\pages 482--485

\crossref{https://doi.org/10.1007/BF02069791}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RZ96200013}

Linking options:

https://www.mathnet.ru/eng/tmf1294

https://www.mathnet.ru/eng/tmf/v103/i1/p170

This publication is cited in the following 14 articles:

R. Ch. Kulaev, A. B. Shabat, “Darboux system and separation of variables in the Goursat problem for a third order equation in $\mathbb {R}^3$ ”, Russian Math. (Iz. VUZ), 64:4 (2020), 35–43
Ekaterina Shemyakova, “Classification of Darboux transformations for operators of the form ∂x∂y+a∂x+b∂y+c”, Illinois J. Math., 64:1 (2020)
S. V. Smirnov, “Factorization of Darboux–Laplace transformations for discrete hyperbolic operators”, Theoret. and Math. Phys., 199:2 (2019), 621–636
David Hobby, Ekaterina Shemyakova, “Classification of Multidimensional Darboux Transformations: First Order and Continued Type”, SIGMA, 13 (2017), 010, 20 pp.
Li S. Shemyakova E. Voronov T., “Differential Operators on the Superline, Berezinians, and Darboux Transformations”, Lett. Math. Phys., 107:9 (2017), 1689–1714
S. V. Smirnov, “Darboux integrability of discrete two-dimensional Toda lattices”, Theoret. and Math. Phys., 182:2 (2015), 189–210
Ekaterina Shemyakova, “Darboux transformations for factorable Laplace operators”, Program Comput Soft, 40:3 (2014), 151
P. G. Grinevich, S. P. Novikov, “Discrete $SL_n$ -connections and self-adjoint difference operators on two-dimensional manifolds”, Russian Math. Surveys, 68:5 (2013), 861–887
S. V. Smirnov, “Semidiscrete Toda lattices”, Theoret. and Math. Phys., 172:3 (2012), 1217–1231
V. G. Marikhin, “Solutions of two-dimensional Schrödinger-type equations in a magnetic field”, Theoret. and Math. Phys., 168:2 (2011), 1041–1047
V. G. Marikhin, “The dressing method and separation of variables: The two-dimensional case”, Theoret. and Math. Phys., 161:3 (2009), 1599–1603
E. A. Kartashova, “A hierarchy of generalized invariants for linear partial differential operators”, Theoret. and Math. Phys., 147:3 (2006), 839–846
A. V. Yurov, “Conjugate chains of discrete symmetries in $(1+2)$ nonlinear equations”, Theoret. and Math. Phys., 119:3 (1999), 731–738
A. I. Zenchuk, “Some generalizations of the 2-dimensional Toda chain and $\operatorname{sh}$ -Gordon equation”, Theoret. and Math. Phys., 110:2 (1997), 183–189

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

Statistics & downloads:
Abstract page:	651
Full-text PDF :	234
References:	86
First page:	2

Что такое QR-код?

Registration to the website

Logotypes