FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 3, PAGES 79-94

**Factorization of loop algebras over
$so(4)$ and integrable nonlinear differential equations**

O.
V.
Efimovskaya

Abstract

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We consider factoring subalgebras for loop algebras over $so(4)$.
Given a factoring subalgebra, we find (in terms of coefficients of
commutator relations) an explicit form of
(1) the corresponding system of the chiral field equation
type, (2) the corresponding two-spin model of the
Landau--Lifshitz equation, and (3) the corresponding
Hamiltonian system of ordinary differential equations with homogeneous
quadratic Hamiltonian and linear $so(4)$-Poisson brackets.

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Last modified: September 14, 2005