As is well known, Korteweg-de Vries equation is a typical one which has planar solitary waves. By considering the higher-dimensional nonlinear waves, we studied a Kadomtsev-Petviashvili (KP) equation and found some interesting results which explain experimental results well enough. Two same amplitude soliton solution of KP equation explain resonance phenomena reported by some experiments. Two arbitrary amplitude soliton solution of KP equation is also obtained in this Letter, which canalsoresultsinresonance phenomena. The phase shift after interaction between two soliton are obtained theoretically in this Letter.It is in agreement with experimental results.

For two-ion-temperature dusty plasma with many dierent dust grains, we derived a Kadomtsev-Petviashvili (KP) equation for unmagnetized, collisionless, hot dusty plasma. We find that in a two-ion-temperature warm dusty plasmas with power law dust size distribution, the velocity of soliton is smaller than that for mono-sized dust plasma which has average dust size. Meanwhile as the temperature of dust plasmas increases, the amplitude of soliton decreases slower than that of mono-sized dust plasma with average dust size, while the width of soliton decreases quicker than that of mono-sized dust plasma with average dust size.

Areasonable normalization for a magnetized dusty plasma with many different dust grains is adopted, which varies self-consistently with the system parameters. A Zakharov-Kuznetsov equation for small but finite am-plitude dust acoustic waves is obtained for magnetized dusty plasma which contains different dust grains by using the reductive perturbation technique. We study the dust size distribution. Some comparisons are made between dusty plasma in which the dust size distribution is considered, and the monosized dusty plasma in which there is only one kind of dust grain whose size is the average dust size. This suggests that both soliton velocity and width are larger than that for monosized dusty plasma, but its amplitude is smaller than that for monosized dusty plasma. If there are positively charged dust grains, compressive solitary waves may exist. The velocity, amplitude, and width of a soliton in multidimensional form for a magnetized dusty plasma which contains many different dust grains are studied as well.