Singularities of Cauchy data, characteristics, cocharacteristics and integral cobordism
A generalization of the classical concept of characteristics for partial differential equations (PDE) is given in the framework of the geometric formal theory for PDEs. In particular, it is given a relation between singularities of Cauchy data and characteristics in order to obtain integral manifolds (solutions) generated by means of characteristics. In this direction it is shown that to any PDE we can associate a ``dual'' equation having the same characteristics. These equations can be related by means of a sort of Bäcklund transformation. Furthermore, a criterion that relates characteristics and integral cobordism (or quantum cobordism) is given. Also a relation between quantum cobordism in nonlinear PDE's and Green's functions is given.
geometry of partial differential equations
scientific article; zbMATH DE number 701735
scientific article