Symmetries and exact solutions via conservation laws for some partial differential equations of Mathematical Physics

Exact solutions of some classical PDEs with two independent variables are achieved by exploiting a double reduction method, which is applied after deducing conserved vectors associated with Lie point symmetries. These are generally obtained through the application of Noether’s theorem, after introducing the notions of adjoint equation and extended Lagrangian. Alternatively associated conserved vectors can be obtained by a direct method.