2 A pr 2 01 4 Twisted reductions of integrable lattice equations , and their Lax representations
نویسندگان
چکیده
It is well known that from two-dimensional lattice equations one can derive one-dimensional lattice equations by imposing periodicity in some direction. In this paper we generalize the periodicity condition by adding a symmetry transformation and apply this idea to autonomous and nonautonomous lattice equations. As results of this approach, we obtain new reductions of the discrete potential Korteweg-de Vries equation, discrete modified Korteweg-de Vries equation and the discrete Schwarzian Korteweg-de Vries equation. We will also describe a direct method for obtaining Lax representations for the reduced equations.
منابع مشابه
A pr 2 00 4 Reductions of integrable equations . Dihedral group
We discuss algebraic and analytic structure of rational Lax operators. With algebraic reductions of Lax equations we associate a reduction group-a group of twisted automor-phisms of the corresponding infinite dimensional Lie algebra. We present a complete study of dihedral reductions for sl(2, C) Lax operators with simple poles and corresponding integrable equations. In the last section we give...
متن کاملSome new integrable equations from the self-dual Yang-Mills equations
Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are nonautonomous versions of the chiral model in (2 + 1) dimensions, generalized nonlinear Schrödinger, Korteweg-de Vries, Toda lattice, Garnier and Euler-Arnold equations. The Lax pairs for all of these equations are derived by the symmetry reductions of ...
متن کاملTowards Noncommutative Integrable Systems
We present a powerful method to generate various equations which possess the Lax representations on noncommutative (1+1) and (1+2)-dimensional spaces. The generated equations contain noncommutative integrable equations obtained by using the bicomplex method and by reductions of the noncommutative (anti-)self-dual Yang-Mills equation. This suggests that the noncommutative Lax equations would be ...
متن کاملv 1 1 8 O ct 1 99 6 Lax Representations and Zero Curvature Representations by Kronecker Product
It is showed that Kronecker product can be applied to construct not only new Lax representations but also new zero curvature representations of integrable models. Meantime a different characteristic between continuous and discrete zero curvature equations is pointed out. Lax representation and zero curvature representation play an important role in studying nonlinear integrable models in theore...
متن کاملSelf-Dual Systems, their Symmetries and Reductions to the Bogoyavlensky Lattice
We recently introduced a class of ZN graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In particular, we introduced a subclass, which we called “self-dual”. In this paper we discuss the continuous symmetries of these systems, their reductions and the relation of the latter to the Bogoyavlensky equation.
متن کامل