  In this paper, we define the modified formal variable separation approach and
show how it determines, in a remarkably simple manner, the decomposition
solutions, the B\"acklund transformations, the Lax pair, and the linear
superposition solution of the B-type Kadomtsev-Petviashvili equation. Also, the
decomposition solutions, the B\"acklund transformation and the Lax pair
relating to the C-type Kadomtsev-Petviashvili equation is obtain by the same
technique. This indicates that the decomposition may provide a description of
integrable behavior in nonlinear systems, while, at the same time, establishing
an efficient method for determining relationships between the particular
systems.
