Partial Differential Equations: Symmetry Generators

In this chapter, the partial differential equations will be treated. Similar to the case of ODEs, there are two basic steps in finding solutions for partial differential equations via symmetry methods: 1) Calculate the symmetry generators 2) Use the generators to construct solutions. The first part, namely calculating the symmetries of the ODEs will be outlined in this chapter and the next chapter is devoted to constructing solutions from the generators. The recursive relations for extended infinitesimal generators will be given. Several sample problems are treated.