Related papers: Recursion operators and bi-Hamiltonian representat…
In this paper we review two concepts directly related to the Lax representations: Darboux transformations and Recursion operators for integrable systems. We then present an extensive list of integrable differential-difference equations…
This paper aims at the most comprehensive and systematic construction and tabulation of mechanical systems that admit a second invariant, quadratic in velocities, other than the Hamiltonian. The configuration space is in general a 2D…
We consider equations arising from rational Lax representations. A general method to construct recursion operators for such equations is given. Several examples are given, including a degenerate bi-Hamiltonian system with a recursion…
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant curvature manifolds and Lie group…
Starting with Lagrangians, which turn out to be degenerate, the Hamiltonian operators for integrable systems can be constructed using Dirac's theory of constraints. We illustrate this by giving a systematic discussion of the first…
We discover multi-Hamiltonian structure of complex Monge-Ampere equation (CMA) set in a real first-order two-component form. Therefore, by Magri's theorem this is a completely integrable system in four real dimensions. We start with…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section,…
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 consider the deformation of the Poincar\'e group in 2+1 dimensions into the quantum double of the Lorentz group and construct Lorentz-covariant momentum-space formulations of the irreducible representations describing massive particles…
We sketch out a new geometric framework to construct Hamiltonian operators for generic, non-evolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, Camassa-Holm equation, and…
D-dimensional constrained systems are studied with stochastic Lagrangian and\break Hamiltonian. It is shown that stochastic consistency conditions are second class constraints and Lagrange multiplier fields can be determined in…
A classification of integrable two-component systems of non-evolutionary partial differential equations that are analogous to the Camassa-Holm equation is carried out via the perturbative symmetry approach. Independently, a classification…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
We report a class of symmetry-intergable third-order evolution equations in 1+1 dimensions under the condition that the equations admit a second-order recursion operator that contains an adjoint symmetry (integrating factor) of order six.…
An extension of the Legendre transform to non-convex functions with vanishing Hessian as a mix of envelope and general solutions of the Clairaut equation is proposed. Applying this to systems with constraints, the procedure of finding a…
We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated…
We studied the constrained Hamiltonian formulation of a supersymmetric Korteweg-de Vries (KdV) equation, which is observed to be a constrained system similar to its classical version. We found a nontrivial Lagrangian description, where we…