Related papers: Functional representations of integrable hierarchi…
Restricting a linear system for the KP hierarchy to those independent variables t\_n with odd n, its compatibility (Zakharov-Shabat conditions) leads to the "odd KP hierarchy". The latter consists of pairs of equations for two dependent…
A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all…
The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by…
The Lax type integrability of a two-component polynomial Burgers type dynamical system within a differential-algebraic approach is studied, its linear adjoint matrix Lax representation is constructed. A related recursion operator and…
A $q$-analogue of the tau function of the modified KP hierarchy is defined by a change of independent variables. This tau function satisfies a system of bilinear $q$-difference equations. These bilinear equations are translated to the…
We obtain via B\"acklund transformation the Hamiltonian representation for a Lax type nonlinear dynamical system hierarchy on a dual space to the Lie algebra of super-integral-differential operators of one anticommuting variable, extended…
In this paper we consider two hierarchies of hereditarily total and continuous functionals over the reals based on one extensional and one intensional representation of real numbers, and we discuss under which asumptions these hierarchies…
A GNS - like *-representation of a \pa\ $\A$ defined by certain representable linear functionals on $\A$ is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads…
It is shown that the Zakharov-Mihailov (ZM) Lagrangian structure for integrable nonlinear equations derived from a general class of Lax pairs possesses a Lagrangian multiform structure. We show that, as a consequence of this multiform…
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
We define a Lax operator as a monic pseudodifferential operator $L(\partial)$ of order $N\geq 1$, such that the Lax equations $\dfrac{\partial L(\partial)}{\partial t_k}=[(L^{\frac kN}(\partial))_+,L(\partial)]$ are consistent and non-zero…
We present (2+1)-dimensional generalizations of the k-constrained Kadomtsev-Petviashvili (k-cKP) hierarchy and corresponding matrix Lax representations that consist of two integro-differential operators. Additional reductions imposed on the…
Explicit KP and AKNS hierarchy equations can be constructed from a certain set of algebraic identities involving a quasi-shuffle product.
We introduce two classes of discrete polynomials and construct discrete equations admitting a Lax representation in terms of these polynomials. Also we give an approach which allows to construct lattice integrable hierarchies in its…
We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group…
We propose a consistently algebraic formulation of the extended KP (supersymmetric) integrable -hierarchy systems. We exploit the results already established in [14] and which consist in a framework suspected to unify in a fascinating way…
We study the expressive power of fragments of inclusion logic under the so-called lax team semantics. The fragments are defined either by restricting the number of universal quantifiers or the arity of inclusion atoms in formulae. In case…
Matrix hierarchies are: multi-component KP, general Zakharov-Shabat (ZS) and its special cases, e.g., AKNS. The ZS comprises all integrable systems having a form of zero-curvature equations with rational dependence of matrices on a spectral…
This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows. We derive a finite…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…