  Bilinearization of a given nonlinear partial differential equation is very
important not only to find soliton solutions but also to obtain other solutions
such as the complexitons, positons, negatons, and lump solutions. In this work
we study the bilinearization of nonlinear partial differential equations in
$(2+1)$-dimensions. We write the most general sixth order Hirota bilinear form
in $(2+1)$-dimensions and give the associated nonlinear partial differential
equations for each monomial of the product of the Hirota operators $D_{x}$,
$D_{y}$, and $D_{t}$. The nonlinear partial differential equations
corresponding to the sixth order Hirota bilinear equations are in general
nonlocal. Among all these we give the most general sixth order Hirota bilinear
equation whose nonlinear partial differential equation is local which contains
12 arbitrary constants. Some special cases of this equation are the KdV, KP,
KP-fifth order KdV, and Ma-Hua equations. We also obtain a nonlocal nonlinear
partial differential equation whose Hirota form contains all possible triple
products of $D_{x}$, $D_{y}$, and $D_{t}$. We give one- and two-soliton
solutions, lump solutions with one, two, and three functions, and hybrid
solutions of local and nonlocal $(2+1)$-dimensional equations. We proposed also
solutions of these equations depending on dynamical variables.
