Exact solutions and branching of singularities for some hyperbolic equations in two variables

Exact global propagators are constructed for the singular hyperbolic operators in two variables , λ a real parameter, and for the degenerate hyperbolic operators . Qualitative phenomena such as uniqueness in the Cauchy problem and branching of singularities vary with λ, as shown earlier by Treves and by Taniguchi and Tozaki.