(2 + 1) dimensional nonlinear waves in a two-ion-temperature warm dusty plasma considering the dust size distribution

For two-ion-temperature dusty plasma with many different 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.