In the previous paper , we have classified generic holonomic systems of general Clairaut type. The notion of holonomic systems of general Clairaut type is one of the generalized notions of the classical Clairaut equations and Clairaut type. We give a generic classification of bifurcations of them as an application of the theory of complete Legendrian unfoldings and transversality theorem. In the list of normal forms, the Lagrangian equation appears. Moreover, there appears several new equations.
"Bifurcations of holonomic systems of general Clairaut type." Hokkaido Math. J. 35 (4) 905 - 934, November 2006. https://doi.org/10.14492/hokmj/1285766435