4 papers
Hierarchy of quantum explicitly solvable and integrable models
A. Pogrebkov
Realizing bosonic field v(x) as current of massless (chiral) fermions we derive hierarchy of quantum polynomial interactions of the field v(x) that are completely integrable and le…
On quantization of the KdV equation
A. Pogrebkov
Quantization procedure of the Gardner-Zakharov-Faddeev and Magri brackets by means of the fermionic representation for the KdV field is considered. It is shown that in both cases t…
On time evolutions associated with the nonstationary Schrödinger equation
A. K. Pogrebkov
The set of integrable symmetries of the nonstationary Schrödinger equation is shown to admit a natural decomposition into subsets of mutually commuting symmetries. Hierarchies of t…
Discrete Schrödinger equation on finite field and associated cellular automaton
A. K. Pogrebkov
The discrete Schrödinger equation with potential belonging to $\F_{2}$ is solved explicitly. On this base the associated (1+1)-dimensional cellular automaton is examined and corres…