Related papers: Classification of integrable Vlasov-type equations
The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method. Analytic asymptotic solutions are constructed in…
TWe suggest a method to construct exactly solvable Gross-Pitaevskii type equations, especially the variable-coefficient high-order Gross-Pitaevskii type equations. We show that there exists a relation between the Gross-Pitaevskii type…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
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.
An analytical solution of the selfconsistent Vlasov equation is presented. The time evolution is entirely determined by the initial distribution function. The largest Lyapunov exponent is calculated analytically. For special parameters of…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
In this work, we study vector-valued functional equations with multiple recursive terms that arise naturally when we are dealing with vector-valued multiplicative Lindley-type recursions. We provide a detailed framework for the solution of…
In the framework of bidifferential graded algebras, we present universal solution generating techniques for a wide class of integrable systems.
Here, in every simple finite-dimensional vectorial Lie superalgebra considered with the standard grading where every indeterminate is of degree 1, the maximal graded solvable subalgebras are classified over $\mathbb{C}$.
We solve a functional equation connected to the algebraic characterization of generalized information functions. To prove the symmetry of the solution, we study a related system of functional equations, which involves two homographies.…
Integrability criterion for the Egorov hydrodynamic type systems is presented. The general solution by generalized hodograph method is found. Examples are given
The problem of group classification of one class of quasilinear equations of hyperbolic type with two independent variables has been solved completely.
The analytical solutions reported in our previous paper are given as series of hypergeometric or Coulomb wave functions. By using them, we can get the Teukolsky functions analytically in a desired accuracy. For the computation, the deep…
Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in…
In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.
The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special…
A new approach to the problem of group classification is applied to the class of first-order non-linear equations of the form $u_a u_a=F(t,u,u_t)$. It allowed complete solution of the group classification problem for a class of equations…
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex…
We present in this paper a new way to define weighted Sobolev spaces when the weight functions are arbitrary small. This new approach can replace the old one consisting in modifying the domain by removing the set of points where at least…
Hypergeometric solutions to seven q-Painlev\'e equations in Sakai's classification are constructed. Geometry of plane curves is used to reduce the q-Painlev\'e equations to the three-term recurrence relations for q-hypergeometric functions.