Authors: O. V. Efimovskaya, V. V. Sokolov

Decompositions of the loop algebra over so(4) are considered, and the exactly integrable nonlinear hyperbolic systems of the principal chiral field equation type are analyzed. New example of such system is found and the Lax representation for this example is constructed.

10 pages, AmS-LaTeX (LaTeX-2e).

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