  This paper examines the properties of a regularization of Burgers equation in
one and multiple dimensions using a filtered convective velocity, which we have
dubbed as convectively filtered Burgers (CFB) equation. A physical motivation
behind the filtering technique is presented. An existence and uniqueness
theorem for multiple dimensions and a general class of filters is proven.
Multiple invariants of motion are found for the CFB equation and are compared
with those found in viscous and inviscid Burgers equation. Traveling wave
solutions are found for a general class of filters and are shown to converge to
weak solutions of inviscid Burgers equation with the correct wave speed.
Accurate numerical simulations are conducted in 1D and 2D cases where the shock
behavior, shock thickness, and kinetic energy decay are examined. Energy
spectrum are also examined and are shown to be related to the smoothness of the
solutions.
