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pro vyhledávání: '"Pogrebkov, A. K."'
Autor:
Pogrebkov, A. K.
In \textit{SIGMA} \textbf{17} (2021), 091, 12 p.p.\ we have presented an integrable system with a negative time variable number for the Davey-Stewartson hierarchy. Here we develop this approach to construct an integrable equation with a lower time va
Externí odkaz:
http://arxiv.org/abs/2410.00211
Autor:
Pogrebkov, Andrei K.
We show that some quantum effects, such as the creation and annihilation of particles and the existence of dark energy, actually arise in study of known models of classical mechanics, such as the Calogero--Moser and Ruijsenaars-Schneider systems.
Externí odkaz:
http://arxiv.org/abs/2407.16018
Autor:
Pogrebkov, Andrei K.
Publikováno v:
SIGMA 17 (2021), 091, 12 pages
We use example of the Davey-Stewartson hierarchy to show that in addition to the standard equations given by Lax operator and evolutions of times with positive numbers, one can consider time evolutions with negative numbers and the same Lax operator.
Externí odkaz:
http://arxiv.org/abs/2106.03835
Autor:
Pogrebkov, A. K.
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:
http://arxiv.org/abs/1904.09469
Autor:
Pogrebkov, Andrei K.
Publikováno v:
SIGMA 13 (2017), 053, 14 pages
Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented. Commutativity
Externí odkaz:
http://arxiv.org/abs/1704.00043
Direct definition of the Cauchy-Jost (known also as Cauchy-Baker-Akhiezer) function in the case of pure solitonic solution is given and properties of this function are discussed in detail using the Kadomtsev-Petviashvili II equation as example. This
Externí odkaz:
http://arxiv.org/abs/1611.04198
Properties of the Cauchy--Jost (known also as Cauchy--Baker--Akhiezer) function of the KPII equation are described. By means of the $\bar\partial$-problem for this function it is shown that all equations of the KPII hierarchy are given in a compact a
Externí odkaz:
http://arxiv.org/abs/1508.02229
Akademický článek
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The Direct and the Inverse Scattering Problems for the heat operator with a potential being a perturbation of an arbitrary $N$ soliton potential are formulated. We introduce Jost solutions and spectral data and present their properties. Then, giving
Externí odkaz:
http://arxiv.org/abs/1212.6793
The heat operator with a general multisoliton potential is considered and its extended resolvent, depending on a parameter $q\in\R^2$ is derived. Its boundedness properties in all variables and its discontinuities in the parameter $q$ are given. As t
Externí odkaz:
http://arxiv.org/abs/1203.4665