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TMF, 2016, Volume 189, Number 3, Pages 323–334 (Mi tmf9209)  

This article is cited in 15 scientific papers (total in 15 papers)

Bäcklund transformations

V. V. Zharinov

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

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.


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

Full text: PDF file (444 kB)
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English version:
Theoretical and Mathematical Physics, 2016, 189:3, 1681–1692

Bibliographic databases:

Document Type: Article
Received: 14.04.2016

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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    Citing articles on Google Scholar: Russian citations, English citations
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    2. V. V. Zharinov, “Lie–Poisson structures over differential algebras”, Theoret. and Math. Phys., 192:3 (2017), 1337–1349  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. B. O. Volkov, “Stochastic Levy differential operators and Yang-Mills equations”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 20:2 (2017), 1750008  crossref  mathscinet  zmath  isi  scopus
    5. 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  mathnet  crossref  crossref  isi  elib  elib
    6. M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133  mathnet  crossref  crossref  isi  elib  elib
    7. Yu. N. Drozhzhinov, “Asymptotically homogeneous generalized functions and some of their applications”, Proc. Steklov Inst. Math., 301 (2018), 65–81  mathnet  crossref  crossref  isi  elib  elib
    8. B. O. Volkov, “Lévy Laplacians in Hida calculus and Malliavin calculus”, Proc. Steklov Inst. Math., 301 (2018), 11–24  mathnet  crossref  crossref  isi  elib  elib
    9. V. V. Zharinov, “Analysis in algebras and modules”, Proc. Steklov Inst. Math., 301 (2018), 98–108  mathnet  crossref  crossref  isi  elib  elib
    10. 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  mathnet  crossref  crossref  isi  elib  elib
    11. A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Proc. Steklov Inst. Math., 301 (2018), 262–271  mathnet  crossref  crossref  isi  elib  elib
    12. V. V. Zharinov, “Analysis in differential algebras and modules”, Theoret. and Math. Phys., 196:1 (2018), 939–956  mathnet  crossref  crossref  adsnasa  isi  elib
    13. N. G. Marchuk, “Classification of extended Clifford algebras”, Russian Math. (Iz. VUZ), 62:11 (2018), 23–27  mathnet  crossref  isi
    14. 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  crossref  isi  scopus
    15. 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  mathnet  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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