  The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an
overarching paradigm for the scaling of nonequilibrium, spatially extended,
classical and quantum systems with strong correlations. Recent analytical
solutions have uncovered a rich structure regarding its scaling exponents and
fluctuation statistics. However, the zero surface tension or zero viscosity
case eludes such analytical solutions and has remained ill-understood. Using
numerical simulations, we elucidate a well-defined universality class for this
case that differs from that of the viscous case, featuring intrinsically
anomalous kinetic roughening, despite previous expectations for systems with
local interactions and time-dependent noise and ballistic dynamics. The latter
may be relevant to recent quantum spin chain experiments which measure KPZ and
ballistic relaxation under different conditions. We identify the ensuing set of
scaling exponents in previous discrete interface growth models related with
isotropic percolation, and show it to describe the fluctuations of additional
continuum systems related with the noisy Korteweg-de Vries equation. Along this
process, we additionally elucidate the universality class of the related
inviscid stochastic Burgers equation.
