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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.

UDC: 517.925.5, 51-73, 537.611.44

MSC: 34G20, 15A90, 15A24

Received: 10.08.2013
Revised: 27.10.2013