arXiv subjects

Anatoly G. Nikitin

Publications and source records attributed to Anatoly G. Nikitin.

5 recordsLinked to original sources

arXiv2011

Generic matrix superpotentials

A simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times2$ and of special superpotentials of dimension $3\times3$ are given explicitly. In addition, a constructive description of superpotentials realized by matrices of arbitrary dimension is presented. In this way an extended class of integrable systems of coupled Schrödinger equation is classified. Examples of such systems are considered in detail. New integrable multidimensional models which are reduced to shape invariant systems via separation of variables are presented also.

math-ph↗

arXiv2005

Generalized Killing Tensors and Symmetry of Klein-Gordon-Fock Equations

The paper studies non-Lie symmetry of the Klein-Gordon-Fock equation (KGF) in $(p+q)$-dimensional Minkowsky space. Full set of symmetry operators for the $n$-order KGF equation was explicitly calculated for arbitrary $n<\infty$ and $p+q \leq 4$. Definition was given for generalized Killing tensors of rank $j$ and order $s$, and for generalized conformal Killing tensors of rank $j$ and order $s$ as a complete set of linearly independent solutions of some overdetermined systems of PDE. These tensors were found in explicit form for arbitrary fixed $j$ and $s$ in Minkowsky space of dimension $p+q \leq 4$. The received results can be used in investigation of higher symmetries of a wide class of systems of partial differential equations.

math-ph↗

arXiv2003

Solitary wave and other solutions for nonlinear heat equations

New exact solutions for the heat equation with a polynomial non-linearity and for the Fisher equation are found. An extended class of non-linear heat equations admitting solitary wave solutions is found. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.

math-ph↗

arXiv2003

Group classification of nonlinear Schrödinger equations

The authors suggest a new powerful tool for solving group classification problems, that is applied to obtaining the complete group classification in the class of nonlinear Schrödinger equations of the form $iψ_t+Δψ+F(ψ,ψ^*)=0$.

math-ph↗

arXiv2002

On the possible types of equations for zero-mass particles

There are a number of papers dedicated to the description of free particles and antiparticles with zero mass and spin 1/2. A great many equations with different C, P, T properties have been proposed and the impression could be formed that there are many nonequivalent theories for zero-mass particles. The purpose or this paper is to show that it is not the case and to describe all nonequivalent equations.

quant-ph↗