On analogs of wave catastrophe functions that are solutions of nonlinear integrable equations

In this paper, we consider symmetry and isomonodromy properties of universal special solutions of integrable nonlinear evolution equations, which are analogs of standard wave catastrophe functions known for linear problems. We perform a comparative analysis of two different approaches to the choice of symmetries of integrable nonlinear equations, which can be applied to the study of such special solutions. Some examples are also presented.