Equivalence groups of differential equations and their applications to mathematical physics problems.

In this paper the notion of a group of equivalence transformations of the family of differential equations is considered. Moreover invariants of Lie groups are investigated. By using these tools some problems from mathematical physics such as: transformations of potential in the nonlinear Schrödinger equation, neutron diffusion problem and relations in Maxwell and material equations have been studied. [ABSTRACT FROM AUTHOR]