Partial Lie-point symmetries of differential equations (Q2713726)

There are considered the partial symmetries of a general differential equation. By means of concrete examples (modified Laplace equation, KdV equation, a nonlinear heat equation, the Boussinesq equation, a partial differential equation admitting a P-Bäcklund symmetry) it is shown how the partial symmetries can be used to obtain solutions. The authors discuss relationships between partial symmetries and the conditional symmetries of Levi and Winternitz and with the conditional generalized symmetries of Zhdanov. The case of dynamical systems is considered. The application of the proposed approach to discrete Lie-point transformations is discussed. The authors noticed that the discrete symmetries should be partial symmetries due to their physical consideration. There are reflections and discrete translations.