Related papers: Lax Pairs for Linear Hamiltonian Systems
This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…
Several examples are given illustrating the (presumably rather general) fact that bosonic Hamiltonians that are supersymmetrizable automatically possess Lax-pairs, and square-roots.
A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure.…
The system of two nonlinear coupled oscillators is studied. As partial case this system of equation is reduced to the Duffing oscillator which has many applications for describing physical processes. It is well known that the inverse…
We establish the algebraic origin of the following observations made previously by the authors and coworkers: (i) A given integrable PDE in $1+1$ dimensions within the Zakharov-Shabat scheme related to a Lax pair can be cast in two…
A kind of Bargmann symmetry constraints involving Lax pairs and adjoint Lax pairs is proposed for soliton hierarchy. The Lax pairs and adjoint Lax pairs are nonlinearized into a hierarchy of commutative finite dimensional integrable…
It is shown that the Lax pair equation dL/dt = [L,A] can be given a neat tensorial interpretation for finite-dimensional quadratic Hamiltonians. The Lax matrices L and A are shown to arise from third rank tensors on the configuration space.…
We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax pair corresponding to a given nonlinear equation is found…
Two simple ways to identify and explain fake Lax pairs are provided. The two methods are complementary, one involves finding a gauge transformation which can be used to remove the associated nonlinear system's dependent variable(s) from a…
By using non-canonical transformation between the Holt system and the Henon-Heiles system the Lax pairs for all the integrable cases of the Holt system are constructed from the known Lax representations for the Henon-Heiles system.
A recipe is presented for obtaining Lax tensors for any n-dimensional Hamiltonian system admitting a Lax representation of dimension n. Our approach is to use the Jacobi geometry and coupling-constant metamorphosis to obtain a geometric Lax…
We use a recently proposed scheme of matrix extension of dispersionless integrable systems for the Abelian case, in which it leads to linear equations, connected with the initial dispersionless system. In the examples considered, these…
A Lax pair for the additive difference Painlev\'e equation of type $E_7^{(1)}$ is explicitly obtained as certain linear difference equations of scalar form. The compatibility of the Lax pair is proved by using certain characterization of…
Given a classical $r$-matrix on a Poisson algebra, we show how to construct a natural family of compatible Poisson structures for the Hamiltonian formulation of Lax equations. Examples for which our formalism applies include the Benny…
We show explicitly how to construct the quantum Lax pair for systems with open boundary conditions. We demonstrate the method by applying it to the Heisenberg XXZ model with general integrable boundary terms.
In this letter, a definition of the higher dimensional Lax pair for a lower dimensional system which may be a chaotic system is given. A special concrete (2+1)-dimensional Lax pair for a general (1+1)-dimensional three order autonomous…
A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients required for the…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic…
We consider non-ultra local linear Poisson algebras on a continuous line . Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or "boundary" extensions. They are…