• Publications
  • Influence
Symmetries of Equations of Quantum Mechanics
Table of
  • 216
  • 14
  • PDF
On approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter
The concept of approximate symmetry is introduced. The authors describe all nonlinearities F(u) with which the nonlinear wave equation Square Operator u+ lambda u3+ epsilon F(u)=0 with a smallExpand
  • 110
  • 10
  • PDF
On a reduction and solutions of nonlinear wave equations with broken symmetry
A generalised definition for invariance of partial differential equations is proposed. Exact solutions of the equations with broken symmetry are obtained.
  • 101
  • 5
The symmetry and some exact solutions of the nonlinear many-dimensional Liouville, d'Alembert and eikonal equations
Multiparametrical exact solutions of the many-dimensional nonlinear d'Alembert, Liouville, sine-Gordon and eikonal equations are obtained. The maximally extensive local invariance groups of theExpand
  • 79
  • 5
  • PDF
On the reduction of the nonlinear multi-dimensional wave equations and compatibility of the d'Alembert-Hamilton system
Abstract The necessary conditions of the compatibility of the d'Alembert-Hamilton system in Minkowsky space R (1,n) are established. The problem of reduction of P(1, n)-invariant wave equations toExpand
  • 29
  • 3
  • PDF
On some new exact solutions of the nonlinear d'Alembert-Hamilton system
Abstract Some new exact solutions of the d'Alembert-Hamilton system of partial differential equations are obtained. The necessary conditions of integrability of an over-determined d'Alembert-HamiltonExpand
  • 22
  • 3
  • PDF
Symmetry and exact solutions of nonlinear spinor equations
Abstract This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differentialExpand
  • 74
  • 1
  • PDF
Reduction and exact solutions of the Navier-Stokes equations
The authors construct a complete set of G(1,3)-inequivalent ansatze of codimension 1 for the Navier-Stokes (NS) field which reduce the NS equations to systems of ordinary differential equationsExpand
  • 31
  • 1
  • PDF