Symmetry in Nonlinear Mathematical Physics - 2009

Valentyn Tychynin (Prydniprovs'ka State Academy of Civil Engineering and Architecture, Dnipropetrovsk, Ukraine)

Nonlocal symmetries and generation solutions formulae to the class of diffusion-convection equations

The wide class of diffusion-convection equations invariant under generalized hodograph transformation is described. For equation that admits linearization, we have constructed new solutions generating formulae, which based on nonlocal transformations and on nonlocal symmetries of linear equation. Formulae of nonlocal nonlinear superposition of solutions to these equations were found. Nonlocal symmetries were used then for construction of chains of exact solutions.