  The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation
with the self-similar Ansatz is analyzed. As a new feature additional analytic
terms are added. From the mathematical point of view, these can be considered
as various noise distribution functions. Six different cases were investigated
among others Gaussian, Lorentzian, white or even pink noise. Analytic solutions
were evaluated and analyzed for all cases. All results are expressible with
various special functions like Kummer, Heun, Whittaker or error functions
showing a very rich mathematical structure with some common general
characteristics.
