Similarity solutions for two-dimensional weak shock waves

The general forms of self-similar solutions for two-dimensional weak shock waves in fluid dynamics are obtained. The functional form describing the area under the initial pulse is characterized under which the general system of PDEs admits similarity solutions. It is shown how one can construct new solutions with shock discontinuity from these self-similar solutions. In particular, a plane-wave solution is joined with a self-similar solution across a non-trivial shock. Furthermore, a new class of non-trivial simple wave solutions is presented.