相关论文: Towards the theory of Benney equations

Some solutions of the Heavenly equations and their generalizations are considered

We summarize results concerning the Bernstein property of differential equations.

Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.

This paper is devoted to a discussion of specific properties of invariants in the theory of forms.

Theoretical predictions on the $B_c$ meson properties are reviewed.

This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…

A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.

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…

Computations in the cohomology of finite groups.

We prove some results on the border of Ramsey theory (finite partition calculus) and model theory. Also a beginning of classification theory of finite models in undertaken.

Theory of $n$-complements with applications is presented.

The work studies some Difference equations, which are connected with Mejer's function.

Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…

We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open…

A general solution to the Complex Bateman equation in a space of arbitrary dimensions is constructed.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…

Special polynomials associated with rational solutions of the second Painlev\'{e} equation and other members of its hierarchy are discussed. New approach, which allows one to construct each polynomial is presented. The structure of the…

The Jacobian algebras are introduced and their various properties are studied.

The first examples of exceptional terminal singularities are constructed.