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Sibirskii Zhurnal Industrial'noi Matematiki
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Sibirskii Zhurnal Industrial'noi Matematiki, 2015, Volume 18, Number 2, Pages 36–47
DOI: https://doi.org/10.17377/sibjim.2015.18.204 (Mi sjim880) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The method of differential relations and nonlinear inverse problems

Yu. E. Anikonovab, M. V. Neshchadimba

a Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
Full-text PDF (616 kB) Citations (4)
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DOI: https://doi.org/10.17377/sibjim.2015.18.204
Abstract: We apply the method of differential relations to the study of some inverse problems for nonlinear one-dimensional differential equations of a general type including the classical equations of soliton theory. We also consider the problem of finding a potential for an equation of continuum mechanics in the one-dimensional case in presence of some differential relation.
Keywords: inverse problems, nonlinear equations, soliton, presentations of solutions.
Received: 16.10.2014
English version:
Journal of Applied and Industrial Mathematics, 2015, Volume 9, Issue 3, Pages 317–327
DOI: https://doi.org/10.1134/S1990478915030035
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: Yu. E. Anikonov, M. V. Neshchadim, “The method of differential relations and nonlinear inverse problems”, Sib. Zh. Ind. Mat., 18:2 (2015), 36–47; J. Appl. Industr. Math., 9:3 (2015), 317–327
Citation in format AMSBIB
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\by Yu.~E.~Anikonov, M.~V.~Neshchadim
\paper The method of differential relations and nonlinear inverse problems
\jour Sib. Zh. Ind. Mat.
\yr 2015
\vol 18
\issue 2
\pages 36--47
\mathnet{http://mi.mathnet.ru/sjim880}
\crossref{https://doi.org/10.17377/sibjim.2015.18.204}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3549826}
\elib{https://elibrary.ru/item.asp?id=23598675}
\transl
\jour J. Appl. Industr. Math.
\yr 2015
\vol 9
\issue 3
\pages 317--327
\crossref{https://doi.org/10.1134/S1990478915030035}
Linking options:
  • https://www.mathnet.ru/eng/sjim880
  • https://www.mathnet.ru/eng/sjim/v18/i2/p36
    • This publication is cited in the following 4 articles:
    1. M. V. Neschchadim, A. A. Simonov, “Backlund transformations of the relativistic Schrodinger equation”, J. Appl. Industr. Math., 17:4 (2023), 828–841  mathnet  crossref  crossref
    2. M. V. Neshchadim, “Bäcklund transformations for the one-dimensional Schrödinger equation”, J. Appl. Industr. Math., 15:2 (2021), 307–314  mathnet  crossref  crossref  elib
    3. Yu. E. Anikonov, N. B. Ayupova, M. V. Neshchadim, “Ray method and questions of identification of the elasticity theory equations”, J. Math. Sci., 246:6 (2020), 738–754  mathnet  crossref  crossref
    4. Yu. E. Anikonov, N. B. Ayupova, “Ray expansions and identities for the second order equations with applications to inverse problems”, J. Math. Sci., 231:2 (2018), 111–123  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский журнал индустриальной математики
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