  We identify the result of the continuous wavelet transform with the
difference of solutions of two hyperbolic partial differential equations, for
which wavelet's shift and scale are considered as independent variables on 2D
plane. The characteristic property, which follows from the introduced
representation is is the fact that the transform's values inside the triangle
defined by two characteristics (a=const, b=const) and crossecting them slopped
line on a scale-shift plane (a,b) are completely and uniquely defined by the
value of transform and its derivatives along the last mentioned line.
