V. V. Zharinov, “Bäcklund transformations”, TMF, 189:3 (2016), 323–334; Theoret. and Math. Phys., 189:3 (2016), 1681

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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 3, Pages 323–334
DOI: https://doi.org/10.4213/tmf9209 (Mi tmf9209)

This article is cited in 20 scientific papers (total in 20 papers)

Bäcklund transformations

V. V. Zharinov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Full-text PDF (444 kB) Citations (20)

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DOI: https://doi.org/10.4213/tmf9209

Abstract: We describe a Bäcklund transformation, i.e., a differentially related pair of differential equations, in a coordinate manner appropriate for calculations and applications. We present several known explanatory examples, including Bäcklund transformations for gauge fields in a Minkowski space of arbitrary dimension.

Keywords: total derivative, partial differential equation, differential relation, constraint, Bäcklund transformation, gauge field, curvature tensor, covariant derivative, Yang–Mills field.

Funding agency	Grant number
Russian Science Foundation	14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.

Received: 14.04.2016

English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 3, Pages 1681–1692
DOI: https://doi.org/10.1134/S0040577916120011

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. V. Zharinov, “Bäcklund transformations”, TMF, 189:3 (2016), 323–334; Theoret. and Math. Phys., 189:3 (2016), 1681–1692

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https://doi.org/10.4213/tmf9209

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This publication is cited in the following 20 articles:

Nida Raees, Irfan Mahmood, Ejaz Hussain, Usman Younas, Hosam O. Elansary, Sohail Mumtaz, “Dynamics of optical solitons and sensitivity analysis in fiber optics”, Physics Letters A, 2024, 130031
V. V. Zharinov, “Binary relations, Bäcklund transformations, and wave packet propagation”, Theoret. and Math. Phys., 205:1 (2020), 1245–1263
A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752
A. K. Gushchin, “On the Existence of $L_2$ Boundary Values of Solutions to an Elliptic Equation”, Proc. Steklov Inst. Math., 306 (2019), 47–65
V. V. Zharinov, “Analysis in Noncommutative Algebras and Modules”, Proc. Steklov Inst. Math., 306 (2019), 90–101
A. K. Gushchin, “A criterion for the existence of $L_p$ boundary values of solutions to an elliptic equation”, Proc. Steklov Inst. Math., 301 (2018), 44–64
M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133
Yu. N. Drozhzhinov, “Asymptotically homogeneous generalized functions and some of their applications”, Proc. Steklov Inst. Math., 301 (2018), 65–81
B. O. Volkov, “Lévy Laplacians in Hida calculus and Malliavin calculus”, Proc. Steklov Inst. Math., 301 (2018), 11–24
V. V. Zharinov, “Analysis in algebras and modules”, Proc. Steklov Inst. Math., 301 (2018), 98–108
N. A. Gusev, “On the definitions of boundary values of generalized solutions to an elliptic-type equation”, Proc. Steklov Inst. Math., 301 (2018), 39–43
A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Proc. Steklov Inst. Math., 301 (2018), 262–271
V. V. Zharinov, “Analysis in differential algebras and modules”, Theoret. and Math. Phys., 196:1 (2018), 939–956
N. G. Marchuk, “Classification of extended Clifford algebras”, Russian Math. (Iz. VUZ), 62:11 (2018), 23–27
M. O. Katanaev, “Description of disclinations and dislocations by the Chern–Simons action for $\mathbb{SO}(3)$ connection”, Phys. Part. Nuclei, 49:5 (2018), 890–893
B. O. Volkov, “Lévy Laplacians and annihilation process”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2018, 399–409
M. O. Katanaev, “Cosmological models with homogeneous and isotropic spatial sections”, Theoret. and Math. Phys., 191:2 (2017), 661–668
V. V. Zharinov, “Lie–Poisson structures over differential algebras”, Theoret. and Math. Phys., 192:3 (2017), 1337–1349
V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736
B. O. Volkov, “Stochastic Levy differential operators and Yang-Mills equations”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:2 (2017), 1750008

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

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