On asymptotic behavior of non-stationary wave field singularities near the space-time caustic

Cauchy problem for wave equation in the case of discontinuity on the initial front is investigated. The discontinuity is given by homogeneous generalized function (degree $\lambda$). The transformation of initial front passed the space-time caustic is examined and as a result uniform wave field asymptotics expressed in terms of polynomial Legendre is obtained.