Related papers: Integrable pseudopotentials related to generalized…
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Using the method of hydrodynamic reductions, we find all integrable infinite (1+1)-dimensional hydrodynamic-type chains of shift one. A class of integrable infinite (2+1)-dimensional hydrodynamic-type chains is constructed.
All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on $\hbar$, and their $\hbar$-dependent extensions. The former group…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
HyperCR Einstein--Weyl equations in 2+1 dimensions reduce to a pair of quasi-linear PDEs of hydrodynamic type. All solutions to this hydrodynamic system can be in principle constructed from a twistor correspondence, thus establishing the…
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…
The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A…
We show that the one dimensional unitary matrix model with potential of the form $a U + b U^2 + h.c.$ is integrable. By reduction to the dynamics of the eigenvalues, we establish the integrability of a system of particles in one space…
We explain how to use the theory of bidifferential ideals to construct integrable hierarchies of hydrodynamic type.
A generalized Camassa-Holm equation, which describes pseudospherical surfaces, is considered. Using geometric methods, it is demonstrated that the equation is geometrically integrable. Additionally, an infinite hierarchy of conservation…
We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole periodic table and we present a complete table of pseudopotential…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
In flux compactifications of M-theory a superpotential is generated whose explicit form depends on the structure group of the 7-dimensional internal manifold. In this note, we discuss superpotentials for the structure groups: G_2, SU(3) or…
Original English Summary. - A systematic method of constructing potentials, for which the one-variable Schroedinger equation can be solved in terms of the hypergeometric (HGM) function, is presented. All the potentials, obtained by…
A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean…
A simple construction of Whitham type hierarchies in all genera is suggested. Potentials of these hierarchies are written as integrals of hypergeometric type. Possible generalization for universal moduli space is also briefly discussed.
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…