  The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation
with the traveling-wave 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 are evaluated and analyzed for all cases. All results are
expressible with various special functions Mathieu, Bessel, Airy or Whittaker
functions showing a very rich mathematical structure with some common general
characteristics. This study is the continuation of our former work, where the
same physical phenomena was investigated with the self-similar Ansatz. The
differences and similarities among the various solutions are enlightened.
