Opanasenko S. Generalized equivalence groups and extended symmetry analysis of differential equations

The thesis is devoted to development of methods for group classification of classes of differential equations and studying their generalized equivalence groups. Studied are admissible transformations and Lie symmetries of a class of reaction–diffusion equations, a class of general Burgers–Korteweg–de Vries equations and its subclasses of equations with spatial and time coefficients and a class of variable–coefficient Burgers equations. Rigorously constructed for the first time are generalized and extended generalized equivalence groups. A notion of an effective generalized equivalence group is introduced. Several examples of such groups are found and their basic properties are studied. The method of furcate splitting is formalized. Extended symmetry analysis of a system modeling an isothermal drift flux is carried out, and found are all its local solutions, generalized symmetries, cosymmetries, local conservation laws and an infinite family of compatible Hamiltonian structures.