Related papers: Lax Representations for Separable Systems from Ben…
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 reconstruct a rational Lax matrix of size R+1 from its spectral curve (the desingularization of the characteristic polynomial) and some additional data. Using a twisted Cauchy--like kernel (a bi-differential of bi-weight (1-nu,nu)) we…
A review of a new separability theory based on degenerated Poisson pencils and the so-called separation curves is presented. This theory can be considered as an alternative to the Sklyanin theory based on Lax representations and the…
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version of…
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…
Given a graph E we define E-algebraic branching systems, show their existence and how they induce representations of the associated Leavitt path algebra. We also give sufficient conditions to guarantee faithfulness of the representations…
We describe the extension, beyond fundamental representations of the Yang-Baxter algebra, of our new construction of separation of variables bases for quantum integrable lattice models. The key idea underlying our approach is to use the…
We prove that the existence of a dispersionless Lax pair with spectral parameter for a nondegenerate hyperbolic second order partial differential equation (PDE) is equivalent to the canonical conformal structure defined by the symbol being…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
We explain how the spectral curve can be extracted from the ${\cal W}$-representation of a matrix model. It emerges from the part of the ${\cal W}$-operator, which is linear in time-variables. A possibility of extracting the spectral curve…
This paper deals with the spectral problem of the Manakov Santini system. The point Lie symmetries of the Lax pair have been identified. Several similarity reductions arise from these symmetries. An important benefit of our procedure is…
The Lax-Sato approach to the hierarchies of Manakov-Santini type is formalized in order to extend it to a more general class of integrable systems. For this purpose some linear operators are introduced, which must satisfy some integrability…
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…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
This paper develops the technique of constructing Lax representations for PDEs via non-central extensions generated by non-triivial exotic 2-cocycles of their contact symmetry algebras. We show that the method is applicable to the Lax…
The Lax pair for a derivative nonlinear Schr\"{o}dinger equation proposed by Chen-Lee-Liu is generalized into matrix form. This gives new types of integrable coupled derivative nonlinear Schr\"{o}dinger equations. By virtue of a gauge…
A multilinear M-dimensional generalization of Lax pairs is introduced and its explicit form is given for the recently discovered class of time-harmonic, integrable, hypersurface motions.
It is showed that Kronecker product can be applied to construct not only new Lax representations but also new zero curvature representations of integrable models. Meantime a different characteristic between continuous and discrete zero…
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…