Abstract
Using special quasigraded Lie algebras, that could be viewed as deformations of loop algebras, we obtain new hierarchies of integrable nonlinear equations admitting zero-curvature representations. In particular, we obtain integrable hierarchies that generalize the Heisenberg magnet, Landau–Lifshitz, and anisotropic chiral field hierarchies. We also obtain a new type of so(3) anisotropic chiral field equation along with its higher rank generalization.
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