Related papers: General Zakharov-Shabat equations without Lax oper…
A recently observed relation between 'weakly nonassociative' algebras A (for which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent variable in the middle nucleus A' of A) is recalled. For any such algebra there is a…
A Lax operator algebra is constructed for an arbitrary semi-simple Lie algebra over $\mathbb C$ equipped with a $\mathbb Z$-grading, and arbitrary compact Riemann surface with marked points. In this set-up, a treatment of almost graded…
We investigate the algebraic structure of integrable hierarchies that, we propose, underlie models of $W$-gravity coupled to matter. More precisely, we concentrate on the dispersionless limit of the topological subclass of such theories, by…
Consider an ordinary differential equation which has a Lax pair representation A'(x)= [A(x),B(x)], where A(x) is a matrix polynomial with a fixed regular leading coefficient and the matrix B(x) depends only onA(x). Such an equation can be…
Additional symmetries of the $p$-reduced KP hierarchy are generated by the Lax operator $L$ and another operator $M$, satisfying $res (M^n L^{m+n/p})$ = 0 for $1 \leq n \leq p-1$ and $m \geq -1$ with the condition that ${\partial L \over…
Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matrices and derive from it a matrix Riccati hierarchy. The…
The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy). Dispersionless limit of this multi-component hierarchy is considered on the level of the $\tau$-function. The so called dispersionless Hirota equations are obtained from…
The prolongation structure of Zhiber-Mikhailov-Shabat (ZMS) equation is studied by using Wahlquist-Estabrook's method. The Lax-pair for ZMS equation and Riccati equations for pseudopotentials are formulated respectively from linear and…
We introduce integrable multicomponent non-commutative lattice systems, which can be considered as analogs of the modified Gel'fand-Dikii hierarchy. We present the corresponding systems of Lax pairs and we show directly multidimensional…
We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with…
Under the Neumann constraints, each equation of the KdV hierarchy is decomposed into two finite dimensional systems, including the well-known Neumann model. Like in the case of the Bargmann constraint, the explicit Lax representations are…
We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…
The generalized Zakharov-Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studied. This study includes: the properties of…
In our work a hierarchy of integrable vector nonlinear differential equations depending on the functional parameter $r$ is constructed using a monodromy matrix. The first equation of this hierarchy for $r=\alpha(\mathbf{p}^t\mathbf{q})$ is…
Explicit evaluations of matrix-variate gamma and beta integrals in the complex domain by using conventional procedures is extremely difficult. Such an evaluation will reveal the structure of these matrix-variate integrals. In this article,…
In this paper we obtain a new class of transformation formulae (without an explicit presence of a derivative) for the integrals containing products of factors $|\zf|^2$ with respect to two components of a disconnected set on the critical…
We find a new $4\times4$ solution to the $osp_q(1|2)$-invariant Yang-Baxter equation with simple dependence on the spectral parameter and propose $2\times 2$ matrix expressions for the corresponding Lax operator. The general inhomogeneous…
In this paper, we complete the classification of 4 x 4 solutions of the Yang-Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then…
The Lax operator of the Gaudin type models is a 1-form on the classical level. In virtue of the quantization scheme proposed in [Talalaev04] (hep-th/0404153) it is natural to treat the quantum Lax operator as a connection; this connection…
Appropriate restrictions of Lax operators which allows to construction of (2+1)-dimensional integrable field systems, coming from centrally extended algebra of pseudo-differential operators, are reviewed. The gauge transformation and the…