2014/11/02 by Vladimir S. Gerdjikov, V. S. Gerdjikov, D. M. Mladenov +5 · 9 citations
Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Affine Lie algebra #Affine representation #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Integrable system #Lie algebra #Lie conformal algebra #Lie theory #Nonlinear Waves and Solitons #nlin.SI
paper · pdf · doi:10.1063/1.4919672
published in Journal of Mathematical Physics 56(5) (American Institute of Physics) · 26 pages
arxiv created 2014/11/02 · openalex publication_date 2015/05/01 · arxiv updated 2015/06/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We have derived a family of equations related to the untwisted affine Lie algebras Ar(1) using a Coxeter ℤr+1 reduction. They represent the third member of the hierarchy of soliton equations related to the algebra. Applying additional ℤ2-involutions, we also obtain the real Hamiltonian forms of these equations. We also give some particular examples and impose additional reductions.