Investigation Of Several Nonlinear Dust Acoustic Waves

A dusty plasma is a weakly ionized gas containing micro-sized solid particles,electrons,ions and neutral particles.Dusty plasmas show many low-frequency phenomena due to the large mass of dust grains.It attracts extensively research interest because of its importance in understanding many space and astrophysics phenomena as well as the laboratory plasmas.The phase shift of a head-on collision between two dust-acoustic solitary waves in an unmagnetized,collisionless and strongly coupled dusty plasma has been studied analytically and numerically.The application scope of the analytical solution of the phase shift of the head-on collision is given in the present paper by comparing the analytical results and the numerical ones.It is found that the analytical results are valid if both amplitudes of the two solitary waves are small enough.We also find that the coupling parameters play an important role in both head-on collision and the waveform,such as the wave speed,wave amplitude and wave width.It is also found that the wave amplitude and the wave width increase,while the wave propagation speed decreases if the coupling parameter increases.Moreover,the phase shift after head-on collision also increases when the coupling parameter increases.Most of authors have mainly focused on dusty plasma containing only mono-sized dust grains.In practice,the dust grains come in many different sizes and the dust size distribution depends on many kinds of conditions.By using the reductive perturbation method,we have derived a Korteweg-deVries-Burgers(Kd V-Burgers)equation,which can describe a shock wave in a dusty plasma.We have studied several cases with different dust size distribution functions and found that,for all different kind of the dust size distributions,the speed and amplitude of a shock wave considering the dust size distribution are larger than that of the dusty plasma with the averaged dust size;however,the width of a shock wave considering the dust size distribution is smaller than that of the dusty plasma with the averaged dust size.