Artur Sergyeyev's home page
I am an Associate Professor at the Division
of Geometry and Mathematical Physics of Mathematical
at Silesian University in Opava.
My research interests include:
My key recent publication is
symmetries and conservation laws of partial differential systems
Lax pairs, recursion operators, Hamiltonian and symplectic structures
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
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
Here are some links that I use a lot:
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Last updated on December 23, 2018, 1:45 CET