Related papers: Is the classical Bukhvostov-Lipatov model integrab…
In this paper, we give the necessary and sufficient conditions of the integrability of relative Rota-Baxter Lie algebras via double Lie groups, matched pairs of Lie groups and factorization of diffeomorphisms respectively. We use the…
We examine the algebraic complete integrability of Lotka-Volterra equations in three dimensions. We restrict our attention to Lotka-Volterra systems defined by a skew symmetric matrix. We obtain a complete classification of such systems.…
General spin-1/2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are non-integrable in the sense that they possess no nontrivial…
Using twisted commutation relations we show that the quantum sinh-Gordon model on noncommutative space is integrable, and compute the exact two-particle scattering matrix. The model possesses a strong-weak duality, just like its commutative…
The exactly solvable BCS Hamiltonian of superconductivity is considered from several viewpoints: Richardson's ansatz, conformal field theory, integrable inhomogenous vertex models and Chern-Simons theory.
Based on the Lie group theory, the one-parameter Lie group admitted by a Silnikov equation is studied. The result reveals that the Silnikov equation accepts no global analytical non-trivial one-parameter Lie group. In this sense, the…
It is shown that gravity on the line can be described by the two dimensional (2D) Hilbert-Einstein Lagrangian supplemented by a kinetic term for the coframe and a translational {\it boundary} term. The resulting model is equivalent to a…
In the present work we revisit the Salerno model as a prototypical system that interpolates between a well-known integrable system (the Ablowitz-Ladik lattice) and an experimentally tractable non-integrable one (the discrete nonlinear…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
We propose several different types of construction principles for new classes of Toda field theories based on root systems defined on Lorentzian lattices. In analogy to conformal and affine Toda theories based on root systems of semi-simple…
In this letter, the integrability aspects of a generalized Fisher type equation with modified diffusion in (1+1) and (2+1) dimensions are studied by carrying out a singularity structure and symmetry analysis. It is shown that the Painlev\'e…
We present a superconformally invariant and integrable model based on the twisted affine Kac-Moody superalgebra $\hat{osp(2|2)}^{(2)}$ which is the supersymmetrization of the purely bosonic conformal affine Liouville theory recently…
We discuss an interrelation between quantum integrable models and classical soliton equations with discretized time. It appeared that spectral characteristics of quantum integrable systems may be obtained from entirely classical set up.…
In this short review the role of the Hirota equation and the tau-function in the theory of classical and quantum integrable systems is outlined.
We prove that the geodesics equations corresponding to the BGPP metric are integrable in the Liouville sense. The $\mathrm{SO}(3,\mathbb{R})$ symmetry of the model allows to reduce the system from four to two degrees of freedom. Moreover,…
It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: We consider integrable deformations of a non-flat Liouville metric in a…
We prove that all classical affine W-algebras W(g,f), where g is a simple Lie algebra and f is its non-zero nilpotent element, admit an integrable hierarchy of bi-Hamiltonian PDEs, except possibly for one nilpotent conjugacy class in G_2,…
We apply a 3-dimensional approach to describe a new parametrization of the L-operators for the 2-dimensional Bazhanov-Stroganov (BS) integrable spin model related to the chiral Potts model. This parametrization is based on the solution of…
We discuss the applicability of the Boltzmann equation to the classical two-dimensional electron gas. We show that in the presence of both the electron-impurity and electron-electron scattering the Boltzmann equation can be inapplicable and…
The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The…