Related papers: Integrable Discretizations of Chiral Models
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
We prove that the doubly lambda-deformed sigma-models, which include integrable cases, are canonically equivalent to the sum of two single lambda-deformed models. This explains the equality of the exact beta-functions and current anomalous…
The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure can be simplified for *-invariant equations. The…
The doubling of massless Dirac fermions on two-dimensional lattices is theoretically studied. It has been shown that the doubling of massless Dirac fermions on a lattice with broken chiral symmetry is topologically protected even when the…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
We present examples of Lax-integrable multi-dimensional systems of partial differential equations with higher local symmetries. We also consider Lagrangian deformations of these equations and construct variational bivectors on them.
All possible linearly independent local conservation laws for $n$-dimensional diffusion--convection equations $u_t=(A(u))_{ii}+(B^i(u))_i$ were constructed using the direct method and the composite variational principle. Application of the…
A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is…
There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for…
Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant…
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws is discussed. In the generic case, nonlocal conservation…
A manifestly gauge invariant lattice action for nonanomalous chiral models is proposed which leads in the continuum limit to the theory free of doublers.
A method of integrable discretization of the Liouville type nonlinear partial differential equations is suggested based on integrals. New examples of discrete Liouville type models are presented.
Using the developed deformation theory on moduli spaces of quadratic differentials we derive variational formulas for objects associated with generalized $SL(2)$ Hitchin's spectral covers: Prym matrix, Prym bidifferential, Hodge and Prym…
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the…
We have proposed, in our previous papers, a method to characterize integrable discrete soliton equations. In this paper we generalize the method further and obtain a $q$-difference Toda equation, from which we can derive various…
We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship…
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…