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TMF, 1997, Volume 110, Number 3, Pages 339–350 (Mi tmf973)  

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

On some generalizations of the factorization method

I. Z. Golubchik, V. V. Sokolov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: The classical factorization method reduces the system of differential equations $U_t=[U_+,U]$ to the problem of solving algebraic equations. Here $U(t)$ belongs to a Lie algebra $\mathfrak G$ which is the direct sum of subalgebras $\mathfrak G_+$ and $\mathfrak G_-$, where “+” denotes the projection on $\mathfrak G_+$. This method is generalized to the case $\mathfrak G_+\cap\mathfrak G_-\ne\{0\}$. The corresponding quadratic systems are reduced to linear systems with varying coefficients. It is shown that the generalized version of the factorization method is also applicable to systems of partial differential equations of the Liouville type equation.

DOI: https://doi.org/10.4213/tmf973

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English version:
Theoretical and Mathematical Physics, 1997, 110:3, 267–276

Bibliographic databases:

Received: 01.08.1996

Citation: I. Z. Golubchik, V. V. Sokolov, “On some generalizations of the factorization method”, TMF, 110:3 (1997), 339–350; Theoret. and Math. Phys., 110:3 (1997), 267–276

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. Z. Golubchik, V. V. Sokolov, “Integrable equations on $\mathbb Z$-graded Lie algebras”, Theoret. and Math. Phys., 112:3 (1997), 1097–1103  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Ferreira, LA, “Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems”, Communications in Mathematical Physics, 203:3 (1999), 649  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. I. Z. Golubchik, V. V. Sokolov, “One More Kind of the Classical Yang–Baxter Equation”, Funct. Anal. Appl., 34:4 (2000), 296–298  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Leach, PGL, “Symmetry, singularities, and integrability in complex dynamics II. Rescaling and time-translation in two-dimensional systems”, Journal of Mathematical Analysis and Applications, 251:2 (2000), 587  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Leach, PGL, “Symmetry, singularities and integrability in complex dynamics I: The reduction problem”, Journal of Nonlinear Mathematical Physics, 7:4 (2000), 445  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. Bruschi, M, “Solvable and/or integrable and/or linearizable N-body problems in ordinary (three-dimensional) space. I”, Journal of Nonlinear Mathematical Physics, 7:3 (2000), 303  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. Golubchik, IZ, “Generalized operator Yang–Baxter equations, integrable ODEs and nonassociative algebras”, Journal of Nonlinear Mathematical Physics, 7:2 (2000), 184  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    8. Mikhailov, AV, “Integrable ODEs on associative algebras”, Communications in Mathematical Physics, 211:1 (2000), 231  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    9. Bruschi, M, “New solvable nonlinear matrix evolution equations”, Journal of Nonlinear Mathematical Physics, 12 (2005), 97  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    10. Maharaj, A, “Properties of the dominant behaviour of quadratic systems”, Journal of Nonlinear Mathematical Physics, 13:1 (2006), 129  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    11. Leach, PGL, “Decomposing populations”, South African Journal of Science, 104:1–2 (2008), 27  isi
    12. Karasu, A, “Nonlocal symmetries and integrable ordinary differential equations: xuml+3xx center dot+x(3)=0 and its generalizations”, Journal of Mathematical Physics, 50:7 (2009), 073509  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    13. R. A. Atnagulova, O. V. Sokolova, “Factorization problem with intersection”, Ufa Math. J., 6:1 (2014), 3–11  mathnet  crossref  mathscinet  elib
    14. Maharaj A., Leach P.G.L., “Application of Symmetry and Singularity Analyses to Mathematical Models of Biological Systems”, Math. Comput. Simul., 96:SI (2014), 104–123  crossref  mathscinet  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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