Related papers: Why the general Zakharov-Shabat equations form a h…

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…

Isomonodromic deformations are nothing but symmetries of the Zakharov-Shabat (isospectral) hierarchy, both the basic ones (belonging to the hierarchy) and additional, restricted to the submanifold of solutions to the string equation.

In this note I discuss some features of the topological theory obtained from the Zakharov-Shabat (or general sl(2,C)) hierarchy, and comment on some possible physical and/or mathematical interpretations of it.

Spinor fields on surfaces of revolution conformally immersed into 3-dimensional space are considered in the framework of the spinor representations of surfaces. It is shown that a linear problem (a 2-dimensional Dirac equation) related with…

By general case we mean methods able to process simplicial sets and chain complexes not of finite type. A filtration of the object to be studied is the heart of both subjects persistent homology and spectral sequences. In this paper we…

We study the solvability of the general two-dimensional Zakharov-Shabat (ZS) systems with meromorphic potentials by quadrature. These systems appear in application of the inverse scattering transform (IST) to an important class of nonlinear…

The Landau-Lifshitz equation is an example of soliton equations with a zero-curvature representation defined on an elliptic curve. This equation can be embedded into an integrable hierarchy of evolution equations called the Landau-Lifshitz…

The equation of motion for Berkovits' WZW-like open (super)string field theory is shown to be integrable in the sense that it can be written as the compatibility condition ("zero-curvature condition") of some linear equations. Employing a…

Following Natanzon-Zabrodin, we explore the Kadomtsev-Petviashvili hierarchy as an infinite system of mutually consistent relations on the second derivatives of the free energy with some universal coefficients. From this point of view,…

A big-isotropic structure is a generalization of the notion of Dirac structure, due to Vaisman. We discuss the inverse problem of deciding if a vector field is Hamiltonian having a big-isotropic structure as underlying geometry. In [1] we…

A class of exact regular spherically symmetric solutions to the Einstein equation obeying Dymnikova's definition of the vacuumlike state is considered. These solutions, which may be interpreted as black holes, are not only singularity free,…

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…

This paper is dedicated to provide the global solutions of algebro-geometric type for all the equations of a new commuting hierarchy containing the Hunter-Saxton (HS) equation. Our main tools include the zero curvature method to derive the…

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear…

A class of multidimensional integrable hierarchies connected with commutation of general (unreduced) (N+1)-dimensional vector fields containing derivative over spectral variable is considered. They are represented in the form of generating…

We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos. The approach expresses these spectral correlations as part of a closed hierarchy of…

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The…

The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised…

A section of a Hamiltonian system is a hypersurface in the phase space of the system, usually representing a set of one-sided constraints (e.g. a boundary, an obstacle or a set of admissible states). In this paper we give local…

Global properties of static, spherically symmetric configurations of scalar fields of sigma-model type with arbitrary potentials are studied in $D$ dimensions, including space-times containing multiple internal factor spaces. The latter are…