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Publications Influence

Symmetries of Equations of Quantum Mechanics

- A. Nikitin, W. I. Fushchich, V. I. Fushchich
- Physics
- 1 September 1994

Table of

216 14- PDF

Solitary wave and other solutions for nonlinear heat equations

- A. Nikitin, T. Barannyk
- Mathematics, Physics
- 2 March 2003

A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented. An extended class of non-linear heat equations admitting solitary wave… Expand

36 3- PDF

Group Classification of Nonlinear Schrödinger Equations

- A. Nikitin, R. Popovych
- Mathematics, Physics
- 1 August 2001

We propose an approach to problems of group classification. By using this approach, we perform a complete group classification of nonlinear Schrödinger equations of the form iψt + Δψ + F(ψ, ψ*) = 0.

59 1- PDF

Group classification of systems of non-linear reaction–diffusion equations with general diffusion matrix. I. Generalized Ginzburg–Landau equations

- A. Nikitin
- Mathematics
- 1 December 2006

Abstract A group classification of the generalized complex Ginzburg–Landau equations is presented. An approach to group classification of systems of reaction–diffusion equations with general… Expand

31 1- PDF

Kinematical invariance groups of the 3d Schrödinger equations with position dependent masses

- A. Nikitin
- Physics
- 31 August 2017

Kinematical invariance groups of the 3d Schrodinger equations with position dependent masses and arbitrary potentials are classified. All non-equivalent classes of such equations are presented… Expand

14 1

On the new invariance algebras and superalgebras of relativistic wave equations

- W. I. Fushchich, A. Nikitin
- Physics
- 21 February 1987

The authors show that any relativistic wave equations for a particle with mass m>0 and arbitrary spin s is invariant under the Lie algebra of the group GL(2s+1, C). The explicit form of basis… Expand

19 1- PDF

Extended Poincaré parasuperalgebra with central charges and invariant wave equations

- A. Nikitin, A. V. Galkin
- Physics
- 1 December 2000

We describe irreducible representations of the extended Poincare parasuperalgebra (PPSA) which includes an arbitrary number N of parasupercharges, n (n≤{N/2}) central charges and an internal symmetry… Expand

2 1- PDF

Construction and classification of indecomposable finite-dimensional representations of the homogeneous Galilei group

- J. Niederle, A. Nikitin
- Physics
- 1 October 2006

We discuss finite-dimensional representations of the homogeneous Galilei group which, when restricted to its subgroup SO(3), are decomposed to spin 0, 1/2 and 1 representations. In particular we… Expand

9 1- PDF

Systems of reaction diffusion equations and their symmetry properties

- A. Nikitin, Ron J. Wiltshire
- Mathematics
- 22 March 2001

A constructive algorithm is proposed for the investigation of symmetries of partial differential equations. The algorithm is used to present classical Lie symmetries of systems of two nonlinear… Expand

32 1- PDF