Symmetry reductions of a particular set of equations of associativity in twodimensional topological field theory

The WDVV equations of associativity arising in twodimensional topological field theory can be represented, in the simplest nontrivial case, by a single third order equation of the Monge-Ampe`re type. By investigating its Lie point symmetries, we reduce it to various nonlinear ordinary differential equations, and we obtain several new explicit solutions.