Related papers: Dispersionless integrable equations as coisotropic…
The three integrable two-dimensional Henon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable generalizations of all these systems are…
The relations between integrable Poisson algebras with three generators and two-dimensional manifolds are investigated. Poisson algebraic maps are also discussed.
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
The study of integrability of the mathematical physics equations showed that the differential equations describing real processes are not integrable without additional conditions. This follows from the functional relation that is derived…
In the series of recent publications we have proposed a novel approach to the classification of integrable differential/difference equations in 3D based on the requirement that hydrodynamic reductions of the corresponding dispersionless…
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…
An isospectral hierarchy of commutative integrable systems associated with a polynomial spectral problem is proposed. The resulting hierarchy possesses a recursion structure controlled by a hereditary operator. The nonisospectral flows…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries.…
Relativistic integrable field theories like the sine-Gordon equation have an infinite set of conserved charges. In a light-front formalism these conserved charges are closely related to the integrable modified KdV hierarchy at the classical…
Structure and properties of families of critical points for classes of functions $W(z,\bar{z})$ obeying the elliptic Euler-Poisson-Darboux equation $E(1/2,1/2)$ are studied. General variational and differential equations governing the…
The negative integrable hierarchies of shallow water waves and dispersionless Toda lattice equations are considered. The integrability is shown by explicit construction of an infinite set of conservation laws.
We study integrable non-degenerate Monge-Ampere equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded structure, uniquely determining the equations. This is used to deform these heavenly…
We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation, and the short pulse equation. They are related to the…
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…
The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction. The involution property relies on…
We study triples of coisotropic or isotropic subspaces in symplectic vector spaces; in particular, we classify indecomposable structures of this kind. The classification depends on the ground field, which we only assume to be perfect and…
We examine the diffraction properties of lattice dynamical systems of algebraic origin. It is well-known that diverse dynamical properties occur within this class. These include different orders of mixing (or higher-order correlations), the…
We prove that general three- or four-dimensional systems %of differential equations are real-analytically nonintegrable near degenerate equilibria in the Bogoyavlenskij sense under additional weak conditions when the Jacobian matrices have…