  This work deals with the dynamics of higher-order rogue waves in a new
integrable (2+1)-dimensional Boussinesq equation governing the evolution of
high and steep gravity water waves. To achieve this objective, we construct
rogue wave solutions by employing Bell polynomial and Hirota's bilinearization
method, along with the generalized polynomial function. Through the obtained
rogue wave solutions, we explore the impact of various system and solution
parameters in their dynamics. Primarily, these parameters determine the
characteristics of rogue waves, including the identification of their type,
bright or dark type doubly-localized rogue wave structures and spatially
localized rational solitons, and manipulation of their amplitude, depth, and
width. Reported results will be encouraging to the studies on the rogue waves
in higher dimensional systems as well as to experimental investigations on the
controlling mechanism of rogue waves in optical systems, atomic condensates,
and deep water oceanic waves.
