FPM 2005, vol. 11, no. 3, pp. 79-94

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

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