Artur Sergyeyev's home page

Welcome to my Web page!

I am an Associate Professor at the Division of Geometry and Mathematical Physics of Mathematical Institute
at Silesian University in Opava.

My research interests include:

My key recent publication is

A. Sergyeyev, New integrable (3+1)-dimensional systems and contact geometry,
Lett. Math. Phys. 108 (2018), no. 2, 359-376 (arXiv:1401.2122)

The search for partial differential systems in four independent variables (4D or (3+1)D
for short) that are integrable in the sense of soliton theory is a longstanding problem of

mathematical physics as our spacetime is four-dimensional and thus the (3+1)D case is
especially relevant for applications. The above article addresses
this problem and proves
that integrable 4D systems
are significantly less exceptional than it appeared before:
in addition to a
handful of well-known important yet isolated examples like the (anti)
self-dual Yang--Mills equations there is a large new class of integrable (3+1)D systems
with Lax pairs of a novel kind related to contact geometry.

Explicit form of two infinite families of integrable (3+1)D systems from this class
with polynomial and rational Lax pairs is given in the article. For example, system
(40) is a new (and the only known to date) integrable generalization from three to
four independent variables for the Khokhlov--Zabolotskaya equation, also known
as the dispersionless Kadomtsev--Petviashvili equation or the Lin--Reissner--Tsien
equation and having many applications in nonlinear acoustics and fluid dynamics.

You may wish to look at the recent slides (to download the PDF please use this link)
for additional background and motivation before proceeding to the article itself.

If you wish to learn more about my research, you are welcome to visit this web page.

Here are some links that I use a lot:

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Preprint archive:

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Last updated on December 23, 2018, 1:45 CET