Zabrodin, A. V.
Published in
Theoretical and Mathematical Physics

Abstract This is a short review of the Kadomtsev–Petviashvili hierarchies of types \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{B}$$\end{document} and \docum...

Pavlov, V. P. Sergeev, V. M. Shamin, R. V.
Published in
Theoretical and Mathematical Physics

Abstract We construct a Hamiltonian field theory model that combines hydrodynamics and thermodynamics. In this model, the continuity equation and the Euler equation for a potential flow are used as the Hamilton equations; and equations of state (or the Gibbs equations, which are equivalent to them ), as equations of second-class constraints. The Ha...

Du, Dianlou Liu, Yuanyuan Wang, Xue
Published in
Theoretical and Mathematical Physics

Abstract We discuss the stationary potential equations as illustrative examples to explain how to construct integrable symplectic maps via Bäcklund transformations. We first give a terse survey of Bäcklund transformations of the potential KdV equation and the potential fifth-order KdV equation. Then, using Jacobi–Ostrogradsky coordinates, we obtain...

Davydov, A. S. Krasnov, A. A. Kuz’min, V. A.
Published in
Theoretical and Mathematical Physics

Abstract We consider nonperturbative vacuum polarization effects in the supercritical region for a planar Dirac–Coulomb system with a supercritical extended axially symmetric Coulomb source with a charge \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage...

Zhang, Yue Luo, Shunlong
Published in
Theoretical and Mathematical Physics

Abstract Although variance, as one of the most fundamental and ubiquitous quantities in quantifying uncertainty, has been widely used in both classical and quantum physics, there are still new applications awaiting exploration. In this work, by interchanging the roles of the state variable and the observable variable, i.e., by formally regarding an...

Gao, Yang Li, Chuanzhong
Published in
Theoretical and Mathematical Physics

Abstract We consider two different subjects: the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-deformed universal characters \documentclass[12pt]{mi...

Chuburin, Yu. P. Tinyukova, T. S.
Published in
Theoretical and Mathematical Physics

Abstract We consider three one-dimensional superconducting structures: 1) the one with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-wave supercondu...

Nasibov, Sh. M.
Published in
Theoretical and Mathematical Physics

Abstract We study the problem of the absence of global periodic solutions of a nonlinear Schrödinger-type evolution equation with a damped linear term. We prove that in the case where the damping factor is negative, the problem has no global periodic solutions for any initial data, and in the case of a negative damping factor, this is also true for...

Kolokoltsov, V. N.
Published in
Theoretical and Mathematical Physics

Abstract There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles in a large ensemble of identical interacting particles. The resulting equations are generally referred to as nonlinear Schrödinger equation...

Benhassine, A.
Published in
Theoretical and Mathematical Physics

Abstract We give a general and weak sufficient condition that is very close to a necessary and sufficient condition for the existence of a sequence of solutions converging to zero for the partial differential equations known as the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \us...