Effects of dust size distribution on nonlinear waves in a dusty plasma

For two-dimensional unmagnetized dusty plasmas with many differentdust grain species, a Kadomtsev--Petviashvili (KP) equation, amodified KP (mKP) equation and a coupled KP(cKP) equation for small,but finite amplitude dust-acoustic solitary waves are obtained fordifferent physical conditions respectively. The influence of anarbitrary dust size distribution described by a polynomialexpressed function on the properties of dust-acoustic solitary wavesis investigated numerically. How dust size distribution affectsthe sign and the magnitude of nonlinear coefficient A (D) of KP(mKP) equation is also discussed in detail. It is noted thatwhether a compressive or a rarefactive solitary wave exists depends on the dust size distribution in some dustyplasmas.