Related papers: New integrable (3+1)-dimensional systems and conta…
We apply the technique of twisted extensions of infinite-dimensional Lie algebras to find new 3D integrable {\sc pde}s related to the deformations of Lie algebra $\mathbb{R}_N[s]\otimes \mathfrak{w}$ with $N=1, 2$ as well as to the Lie…
For the 3-component dispersionless Boussinesq-type system, we construct two compatible nontrivial finite deformations for the Lie algebra structure in the symmetry algebra.
In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax…
We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases…
The Lax-Sato approach to the hierarchies of Manakov-Santini type is formalized in order to extend it to a more general class of integrable systems. For this purpose some linear operators are introduced, which must satisfy some integrability…
A $2n$-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux…
We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely…
We describe a nonlinear kagome lattice with nonlinear dynamics described by Klein-Gordon interactions with a scalar unknown at each node, such as might occur in a nonlinear electrical lattice. We show that the dispersion relation has three…
A (d+1)-dimensional dispersionless PDE is said to be integrable if its n-component hydrodynamic reductions are locally parametrized by (d-1)n arbitrary functions of one variable. Given a PDE which does not pass the integrability test, the…
In this article, I will report a Lax pair structure, a Backlund-Darboux transformation, and the investigation of homoclinic structures for 2D Euler equations of incompressible inviscid fluids.
The article deals with the problem of the integrable discretization of the well-known Drinfeld-Sokolov hierarchies related to the Kac-Moody algebras. A class of discrete exponential systems connected with the Cartan matrices has been…
Applying an original megaideal-based version of the algebraic method, we compute the point-symmetry pseudogroup of the dispersionless (potential symmetric) Nizhnik equation. This is the first example of this kind in the literature, where…
Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…
The Lax type integrability of a two-component polynomial Burgers type dynamical system within a differential-algebraic approach is studied, its linear adjoint matrix Lax representation is constructed. A related recursion operator and…
An N=1 supersymmetric extension of the Ruijsenaars-Schneider three-body model is constructed and its integrability is established. In particular, three functionally independent Grassmann-odd constants of the motion are given and their…
A three-by-three matrix spectral problem for AKNS soliton hierarchy is proposed and the corresponding Bargmann symmetry constraint involved in Lax pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax systems possess…
We develop the symbolic representation method to derive the hierarchies of $(2+1)$-dimensional integrable equations from the scalar Lax operators and to study their properties globally. The method applies to both commutative and…
We study four particular 3-dimensional natural Hamiltonian systems defined in conformally Euclidean spaces. We prove their superintegrability and we obtain, in the four cases, the maximal number of functionally independent integrals of…
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the…
We introduce a class of integrable dynamical systems of interacting classical matrix-valued fields propagating on a discrete space-time lattice, realized as many-body circuits built from elementary symplectic two-body maps. The models…