Zobrazeno 1 - 10
of 84
pro vyhledávání: '"A. K. Pogrebkov"'
Autor:
Andrei K. Pogrebkov
Publikováno v:
Mathematics, Vol 9, Iss 16, p 1988 (2021)
The Kadomtsev–Petviashvili equation is known to be the leading term of a semi-infinite hierarchy of integrable equations with evolutions given by times with positive numbers. Here, we introduce new hierarchy directed to negative numbers of times. T
Externí odkaz:
https://doaj.org/article/6c946c2b567e4a9698353e1ab46019d8
Autor:
Iskander A. Taimanov, Nikita Nekrasov, Petr Georgievich Grinevich, O. K. Sheinman, Sergey Novikov, M. A. Olshanetsky, A. N. Varchenko, Leonid Chekhov, S. Yu. Dobrokhotov, Semen Bensionovich Shlosman, Andrei Marshakov, Andrei Mironov, Aleksandr Petrovich Veselov, Michael Anatol'evich Tsfasman, Viktor M Buchstaber, A. K. Pogrebkov, S. M. Grushevsky, Anton Zabrodin, A. Yu. Okounkov
Publikováno v:
Russian Mathematical Surveys. 76:733-743
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3dfeb8e19d731f0c0aa6b329fd0467e4
https://doi.org/10.1070/rm10015
https://doi.org/10.1070/rm10015
Autor:
A. K. Pogrebkov
Publikováno v:
Theoretical and Mathematical Physics. 205:1585-1592
The approach based on commutator identities for elements of associative algebras was previously effectively used to investigate $$(2{+}1)$$ -dimensional integrable systems. We develop this approach to investigate integrable hierarchies and their rela
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::93091241855984552c04ee4fa3bdfe00
https://doi.org/10.1134/s004057792012003x
https://doi.org/10.1134/s004057792012003x
Autor:
A. K. Pogrebkov
Publikováno v:
Theoretical and Mathematical Physics. 204:1201-1208
We realize an example of induced dynamics using new multiplicative determinant relations whose roots give the particle positions. We present both a general scheme for describing completely integrable dynamical systems parameterized by an arbitrary $$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::33397e694dbcfb2c04f50714faab8ef1
https://doi.org/10.1134/s0040577920090081
https://doi.org/10.1134/s0040577920090081
Autor:
A. K. Pogrebkov
Publikováno v:
Theoretical and Mathematical Physics. 197:1779-1796
We previously proposed an approach for constructing integrable equations based on the dynamics in associative algebras given by commutator relations. In the framework of this approach, evolution equations determined by commutators of (or similarity t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::41714880b8bc9f7b1f46b0436ebf5d11
https://doi.org/10.1134/s0040577918120085
https://doi.org/10.1134/s0040577918120085
Publikováno v:
Russian Mathematics. 62:50-58
We discuss the problems of the connections of the modern theory of integrability and the corresponding overdetermined linear systems with works of geometers of the late nineteenth century. One of these questions is the generalization of the theory of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::535c0db57b588158fdf4c1571624de30
https://doi.org/10.3103/s1066369x18120046
https://doi.org/10.3103/s1066369x18120046
Publikováno v:
Proceedings of the Steklov Institute of Mathematics. 302:250-269
For a Darboux system in ℝ3, we introduce a class of solutions for which an auxiliary second-order linear problem satisfies the factorization condition. We show that this reduction provides the (local) solvability of the Darboux system, and present
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::163901f5d20e3ff03a8c52089c257435
https://doi.org/10.1134/s0081543818060123
https://doi.org/10.1134/s0081543818060123
Autor:
A. K. Pogrebkov
Publikováno v:
Teoreticheskaya i Matematicheskaya Fizika. 197:444-463
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1793325141e971d13c11b41cb0da58da
https://doi.org/10.4213/tmf9569
https://doi.org/10.4213/tmf9569
Autor:
A. K. Pogrebkov
Publikováno v:
Symmetry
Volume 11
Issue 3
Symmetry, Vol 11, Iss 3, p 436 (2019)
Volume 11
Issue 3
Symmetry, Vol 11, Iss 3, p 436 (2019)
We considered the relation between two famous integrable equations: The Hirota difference equation (HDE) and the Darboux system that describes conjugate curvilinear systems of coordinates in R 3 . We demonstrated that specific properties of solutions
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ea457b2dc7918438f56db84cd1636255
Autor:
A. K. Pogrebkov
Induced dynamics is defined as dynamics of real zeros with respect to $x$ of equation $f(q_1-x,\ldots,q_N-x,p_1,\ldots,p_N)=0$, where $f$ is a function, and $q_i$ and $p_j$ are canonical variables obeying some (free) evolution. Identifying zero level
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4761effab63c9755c8dd701c4bf6e8d4
