We give an extensive analytical study of a class of linear growth equations in 1+1 dimensions which describe certain interfacial super-roughening processes. With our calculation, we give a first rigorous analytical affirmation on the applicability of the anomalous dynamic scaling ansatz, which has been proposed to describe the dynamics of super-rough interfaces in finite systems. In addition, we explicitly evaluate not only the leading order but also all the sub-leading orders which dominate over the ordinary dynamic scaling term. Finally, we briefly discuss the influence of the macroscopic background formation on the interfacial anomalous roughening in super-rough growth processes.
International Journal of Modern Physics B 15(26), pp.3429-3438