Twisted Quantum Lax Equations

2 A pr 2 01 4 Twisted reductions of integrable lattice equations , and their Lax representations

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 Kor...

Twisted Yang-Baxter equations for linear quantum (super)groups

We consider the modified (or twisted) Yang-Baxter equations for the SLq(N) groups and SLq(N |M) supergroups. The general solutions for these equations are presented in the case of the linear quantum (super)groups. The introduction of spectral parameters in the twisted Yang-Baxter equation and its solutions are also discussed. Permanent address: Bogoliubov Laboratory of Theoretical Physics, JINR...

Quantum Twisted Codes

Approximated Lax Pair for Nonlinear Evolution Equations

The purpose of this talk will be to present a new reduced-order modelling approach to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, the basis on which the solution is searched for evolves in time according to a dynamics specific to the problem. It is therefore well-suited to solving prob...

Integrable boundary conditions and modified Lax equations

We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding “transfer” matrices give rise to time evolution equations for the initial Lax operator. We systematically identify the modified Lax pairs for both discrete and continuum boundary integrable models, depending on the classical r-matrix an...