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 Nelin. Dinam., 2014, Volume 10, Number 1, Pages 35–48 (Mi nd423)

Matrix functional substitutions for integrable dynamical systems and the Landau–Lifshitz equations

Victor M. Zhuravlev

Ulyanovsk State University, Leo Tolstoy str. 42, Ulyanovsk, 432017, Russia

Abstract: The paper sets out the main elements of the theory of matrix functional substitutions to the construction of integrable finite-dimensional dynamical systems and the application of this theory to the integration of the Landau–Lifshitz equation for a homogeneous magnetic field in the external variable fields. Developed a general scheme for constructing solutions and is an example of the construction of the exact solution for a circularly polarized field.

Keywords: integrable finite-dimensional dynamical systems, matrix functional substitutions, Landau–Lifshitz equations.

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UDC: 517.925.5, 51-73, 537.611.44
MSC: 34G20, 15A90, 15A24
Revised: 27.10.2013

Citation: Victor M. Zhuravlev, “Matrix functional substitutions for integrable dynamical systems and the Landau–Lifshitz equations”, Nelin. Dinam., 10:1 (2014), 35–48

Citation in format AMSBIB
\Bibitem{Zhu14} \by Victor~M.~Zhuravlev \paper Matrix functional substitutions for integrable dynamical systems and the Landau--Lifshitz equations \jour Nelin. Dinam. \yr 2014 \vol 10 \issue 1 \pages 35--48 \mathnet{http://mi.mathnet.ru/nd423}