The concept of approximate symmetry is introduced. The authors describe all nonlinearities
F (u) with which the nonlinear wave equation Square Operator u+ lambda u 3+ epsilon F …

We present a survey of results regarding the investigation of the conditions of the symmetry
of nonlinear equations of mathematical and theoretical physics: the wave equation, the …

Conditional invariance and exact solutions of the nonlinear equation Page 1 II ~ (~) II Re -t~-a'4Mw~+~c''+rl~x"~"-~
11 So (8) I1 (32) for all x10. We assume that g0 and d are so small that 4A4 V~d + ~ (8) + II H …

Sufficient reduction conditions for partial differential equations possessing nontrivial
conditional symmetry are established. The results obtained generalize the classical …

A constructive method is given for the integration of the overdetermined system of nonlinear
d'Alembert wave and eikonal equations□ u= F 1 (u), u xµ u xµ= F 2 (u). With the aid of this …

We present a survey of development of the concept of hidden symmetry in the field of partial
differential equations, including a series of results previously obtained by the author. We …

Symmetry and non-lie reduction of the nonlinear Schrödinger equation Page 1
SYMMETRY AND NON-LIE REDUCTION OF THE NONLINEAR SCHRODINGER EQUATION …

The concept of canonical decomposition of an arbitrary subalgebra of the algebra AO (1, n)
is introduced. With the help of this decomposition all maximal subalgebras L of rank n− 1 of …

We study the problem of group classification of quasilinear elliptic equations in a two-
dimensional space. The list of all equations of this type admitting solvable Lie algebras of …

We present the group classification of one class of (1+ 3)-dimensional nonlinear boundary-
value problems of the Stefan type that simulate the processes of melting and evaporation of …