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Sibirskii Zhurnal Industrial'noi Matematiki, 2014, Volume 17, Number 4, Pages 31–37 (Mi sjim856)  
This article is cited in 5 scientific papers (total in 5 papers)

The Hopf–Cole transformation and multidimensional representations of solutions to evolution equations

Yu. E. Anikonova, N. B. Ayupovaba

a Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
Full-text PDF (219 kB) Citations (5)
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Abstract: We consider new identities and representations of solutions to second-order differential equations connected with the Hopf–Cole transformation.
Keywords: inverse problem, evolution equation, Hopf–Cole transformation.
Received: 06.05.2014
English version:
Journal of Applied and Industrial Mathematics, 2015, Volume 9, Issue 1, Pages 11–17
DOI: https://doi.org/10.1134/S1990478915010020
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: Yu. E. Anikonov, N. B. Ayupova, “The Hopf–Cole transformation and multidimensional representations of solutions to evolution equations”, Sib. Zh. Ind. Mat., 17:4 (2014), 31–37; J. Appl. Industr. Math., 9:1 (2015), 11–17
Citation in format AMSBIB
\Bibitem{AniAyu14}
\by Yu.~E.~Anikonov, N.~B.~Ayupova
\paper The Hopf--Cole transformation and multidimensional representations of solutions to evolution equations
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 4
\pages 31--37
\mathnet{http://mi.mathnet.ru/sjim856}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3364390}
\transl
\jour J. Appl. Industr. Math.
\yr 2015
\vol 9
\issue 1
\pages 11--17
\crossref{https://doi.org/10.1134/S1990478915010020}
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  • https://www.mathnet.ru/eng/sjim856
  • https://www.mathnet.ru/eng/sjim/v17/i4/p31
    • This publication is cited in the following 5 articles:
    1. Ying Chen, Xi Liu, Zhenhua Chai, Baochang Shi, “A Cole–Hopf Transformation Based Fourth-Order Multiple-Relaxation-Time Lattice Boltzmann Model for the Coupled Burgers' Equations”, J Sci Comput, 103:1 (2025)  crossref
    2. Fumei Rong, Qianhuan Li, Baochang Shi, Zhenhua Chai, “A lattice Boltzmann model based on Cole-Hopf transformation for N-dimensional coupled Burgers' equations”, Computers & Mathematics with Applications, 134 (2023), 101  crossref
    3. Yu. E. Anikonov, M. V. Neshchadim, “Generalized Cole–Hopf transformation”, J. Appl. Industr. Math., 12:3 (2018), 409–416  mathnet  crossref  crossref  elib  elib
    4. 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
    5. 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
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