相关论文: Recursion Operator and Rational Lax Representation
An integrable system is often formulated as a flat connection, satisfying a Lax equation. It is given in terms of compatible systems having a common solution called the ``wave function" $\Psi$ living in a Lie group $G$, which satisfies some…
It is shown that the generalized Riemann equation is equivalent with the multicomponent generalization of the Hunter - Saxton equation. New matrix and scalar Lax representation is presented for this generalization. New class of 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…
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
We study the deformed Harry Dym and Hunter-Zheng equations with two arbitrary deformation parameters. These reduce to various other known models in appropriate limits. We show that both these systems are bi-Hamiltonian with the same…
We give a Lax description for the system of polytropic gas equations. The special structure of the Lax function naturally leads to the two infinite sets of conserved charges associated with this system. We obtain closed form expressions for…
We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function.…
For one dimensional SU(n) Hubbard model, a pair of Lax operators are derived, which give a set of fundamental equations for the quantum inverse scattering method under both periodic and open boundary conditions. This provides another proof…
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.…
A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related…
An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
We show how to use operators in the description of {\em exchanging processes} often taking place in (complex) classical systems. In particular, we propose a set of rules giving rise to an {\em hamiltonian} operator for such a system $\Sc$,…
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…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
Pseudodifferential operators of several variables are formal Laurent series in the formal inverses of $\partial_1, ..., \partial_n$ with $\partial_i = d$ $1 \leq i \leq n$. As in the single variable case, Lax equations can be constructed…
We describe the solutions to a family of rotationally symmetric second order partial differential equations in the complex plane that arises from a four-dimensional complex Lie algebra whose spanning set generates the algebra from which…
We propose a recursive algorithm for the calculation of multi-baryon correlation functions that combines the advantages of a recursive approach with those of the recently proposed unified contraction algorithm. The independent components of…
It is explained how the time evolution of the operadic variables may be introduced. As an example, an operadic Lax representation of the harmonic oscillator is considered.