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

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

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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:
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