Related papers: Multi-component Hamiltonian difference operators
We present two different hamiltonian extensions of the Degasperis - Procesi equation to the two component equations. The construction based on the observation that the second Hamiltonian operator of the Degasperis - Procesi equation could…
Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…
We develop the notions of multiplicative Lie conformal and Poisson vertex algebras, local and non-local, and their connections to the theory of integrable differential-difference Hamiltonian equations. We establish relations of these…
We present first heavenly equation of Pleba\'nski in a two-component evolutionary form and obtain Lagrangian and Hamiltonian representations of this system. We study all point symmetries of the two-component system and, using the inverse…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
An overview of Hamiltonian systems with noncanonical Poisson structures is given. Examples of bi-Hamiltonian ode's, pde's and lattice equations are presented. Numerical integrators using generating functions, Hamiltonian splitting,…
Computation of homology or cohomology is intrinsically a problem of high combinatorial complexity. Recently we proposed a new efficient algorithm for computing cohomologies of Lie algebras and superalgebras. This algorithm is based on…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
It is shown that the new Poisson brackets proposed in Part I of this work (J. Math. Phys. 34, 5747(hep-th/9305133)) arise naturally in an extension of the formal variational calculus incorporating divergences. The linear spaces of local…
This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an…
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
We consider the Lie-algebraic notion of commutant in the setting of Poisson algebra. This provides a framework for deforming Hamiltonian differential equations. By taking a subalgebra of the algebra of integrals, and considering the set of…
We first introduce the notion of Hamiltonian structure for a partial difference equation. Then we construct some infinite quivers, and realize the discrete KdV equation, the Hirota-Miwa equation and its various reductions as the mutation…
The Oriented Associativity equation plays a fundamental role in the theory of Integrable Systems. In this paper we prove that the equation, besides being Hamiltonian with respect to a first-order Hamiltonian operator, has a third-order…
Elementary properties of the Koornwinder-Macdonald multivariable Askey-Wilson polynomials are discussed. Studied are the orthogonality, the difference equations, the recurrence relations, and the orthonormalization constants for these…
We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, a family of Hamiltonians that belong to the same phase of matter is described by a map between modules…
We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach…