  Whitham modulation theory for certain two-dimensional evolution equations of
Kadomtsev-Petviashvili (KP) type is presented. Three specific examples are
considered in detail: the KP equation, the two-dimensional Benjamin-Ono (2DBO)
equation and a modified KP (m2KP) equation. A unified derivation is also
provided. In the case of the m2KP equation, the corresponding Whitham
modulation system exhibits features different from the other two. The approach
presented here does not require integrability of the original evolution
equation. Indeed, while the KP equation is known to be a completely integrable
equation, the 2DBO equation and the m2KP equation are not known to be
integrable. In each of the cases considered, the Whitham modulation system
obtained consists of five first-order quasilinear partial differential
equations. The Riemann problem (i.e. the analogue of the Gurevich-Pitaevskii
problem) for the one-dimensional reduction of the m2KP equation is studied. For
the m2KP equation, the system of modulation equations is used to analyze the
linear stability of traveling wave solutions.
