28 citations · 81 across the 13 of their papers we have counts for
13 papers
Integrable equations with negative evolution numbers
Andrei Pogrebkov
Two integrable systems are constructed in a 2 + 1-dimensional space. Every of these systems involve two evolutions with negative numbers.
Equation with the lower negative time number in the Davey--Stewartson hierarchy
A. K. Pogrebkov
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…
Quantum aspect of the classical dynamics
Andrei K. Pogrebkov
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 mechani…
Negative Times of the Davey-Stewartson Integrable Hierarchy
Andrei K. Pogrebkov
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 con…
Induced dynamics
A. K. Pogrebkov
Induced dynamics is defined as dynamics of real zeros with respect to of equation , where is a function, and and are can…
Symmetries of the Hirota Difference Equation
Andrei K. Pogrebkov
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…