Related papers: Moyal Noncommutative Integrability and the Burgers…
Noncommutative Euclidean spaces -- otherwise known as Moyal spaces or quantum Euclidean spaces -- are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the…
In Ref.~\cite{Sag} we proposed a geometric formulation of generalized Nambu mechanics. In the present paper we extend the class of Nambu systems by replacing the stringent condition of constancy of 3-form by closedness. We also explore the…
We study a class of noncommutative gauge theory models on 2-dimensional Moyal space from the viewpoint of matrix models and explore some related properties. Expanding the action around symmetric vacua generates non local matrix models with…
We formulate the conformal mapping between $R^3$ and $S^3$, the 3 sphere. This mapping is applied to the critical Ising model. From this mapping, we calculate the second and fourth moments of the magnetization density, and using those…
This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the…
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other…
Conformal symmetry underlies the mathematical description of various two-dimensional integrable models (e.g. for their Lax representation, Poisson algebra, zero curvature representation,...) or of conformal models (for the anomalous Ward…
We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems.…
We discuss the double copy formulation of Moyal-Weyl type noncommutative gauge theories from the homotopy algebraic perspective of factorisations of $L_\infty$-algebras. We define new noncommutative scalar field theories with rigid colour…
A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space-time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete symmetries for the lattice Maxwell system. As a result,…
A linear system, which generates a Moyal-deformed two-dimensional soliton equation as integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The…
We explore new symmetries in two-component third-order Burgers' type systems in (1+1)-dimension using Wang's O-scheme. We also find a master symmetry for a (2+1)-dimensional Davey-Stewartson type system. These results shed light on the…
Two-dimensional compounds with non-zero Berry curvature are ideal systems to study exotic and technologically favourable thermoelectric and magnetoelectric properties. Within this class of materials, the topological trivial and non-trivial…
This paper treats nonlinear wave current interactions in their simplest form, as an overtaking collision. In one spatial dimension, the paper investigates the collision interaction formulated as an initial value problem of a Burgers bore…
With the aim of exploring a massive model corresponding to the perturbation of the conformal model [hep-th/0211094] the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is…
We study the Moyal evolution of the canonical position and momentum variables. We compare it with the classical evolution and show that, contrary to what is commonly found in the literature, the two dynamics do not coincide. We prove that…
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and…
We present a mechanism to construct four-dimensional charged massless Ramond states using the discrete states of a fivebrane Liouville internal conformal field theory. This conformal field theory has background charge, and admits an inner…