Related papers: Integrable Discretizations of Chiral Models
In the context of integrable field theory with boundary, the integrable non-linear sigma models in two dimensions, for example, the $O(N)$, the principal chiral, the ${\rm CP}^{N-1}$ and the complex Grassmannian sigma models are discussed…
Matrix differential-difference Lax pairs play an essential role in the theory of integrable nonlinear differential-difference equations. We present sufficient conditions which allow one to simplify such a Lax pair by matrix gauge…
The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature…
For all non-symmetric discrete relativistic Toda type equations we establish a relation to 3D consistent systems of quad-equations. Unlike the more simple and better understood symmetric case, here the three coordinate planes of $\mathbb…
A bicomplex structure is associated to the Leznov-Saveliev equation of integrable models. The linear problem associated to the zero curvature condition is derived in terms of the bicomplex linear equation. The explicit example of a…
We consider a nonlinear field equation which can be derived from a binomial lattice as a continuous limit. This equation, containing a perturbative friction-like term and a free parameter $\gamma$, reproduces the Toda case (in absence of…
We derive conservation laws for Dirac-harmonic maps and their extensions to manifolds that have isometries, where we mostly focus on the spherical case. In addition, we discuss several geometric and analytic applications of the latter.
We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…
A simple approximate treatment of statistical equilibrium is developed within the linear sigma sigma model by means of the Hartree factorization technique, providing a simple means for sampling initial configurations of the chiral field.…
In our previous work \cite{LNS}, we constructed quasi-Casoratian solutions to the noncommutative $q$-difference two-dimensional Toda lattice ($q$-2DTL) equation by Darboux transformation, which we can prove produces the existing Casoratian…
We introduce a so-called `coprimeness-preserving non-integrable' extension (another terminology is `quasi-integrable' extension) to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such…
A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference…
We apply the direct method of obtaining reductions to the Toda hierarchy of equations. The resulting equations form a hierarchy of ordinary differential difference equations, also known as delay-differential equations. Such a hierarchy…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
An intrinsic version of the integrability theorem for the classical Backlund theorem is presented. It is characterized by a one-form which can be put in the form of a Riccati system. It is shown how this system can be linearized. Based on…
In this paper we consider affine Toda systems defined on the half-plane and study the issue of integrability, i.e. the construction of higher-spin conserved currents in the presence of a boundary perturbation. First at the classical level…
This paper describes a lattice version of the Skyrme model in 2+1 and 3+1 dimensions. The discrete model is derived from a consistent discretization of the radial continuum problem. Subsequently, the existence and stability of the skyrmion…
We discuss the concept of Lax-Darboux scheme and illustrate it on well known examples associated with the Nonlinear Schrodinger (NLS) equation. We explore the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model,…
We address the problem of classification of integrable differential-difference equations in 2+1 dimensions with one/two discrete variables. Our approach is based on the method of hydrodynamic reductions and its generalisation to dispersive…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…