The operator is bilinear, or linear in either one of its arguments if the other is held fixed. Considering the first argument, for any constants and ,
Another important property (for lack of a better term, it will be called ``triple self-adjointness" in this article) is that for any three functions , and defined over the quarter plane
,
In designing a conservative numerical scheme for (11.1), it is crucial that discrete analogues of the properties (11.4) and (11.5) be maintained. The bilinear property (11.3) is the key to efficient computer realizations, as will be discussed in Section 11.2.2.